ืคึผืจืึธื”ืึธืกื˜ืขืจ > ื‘ืœืึธื’ > ืื™ื ื˜ืขืจื ืขื˜ ื ื™ื™ึทืขืก > ืœื•ื™ืฃ "ืคืึทื ื“ืึทืžืขื ื˜ืึทืœื– ืคื•ืŸ ืขืคืขืงื˜ื™ื•ื• ืึทืจื‘ืขื˜ ืžื™ื˜ Wolfram ื˜ืขืงื ืึทืœืึทื“ื–ืฉื™ื–": ืžืขืจ ื•ื•ื™ 13 ืฉืขื” ืคื•ืŸ ื•ื•ื™ื“ืขื ืจืขืคึฟืขืจืึทื˜ืŸ, ื˜ืขืึธืจื™ืข ืื•ืŸ ื˜ืึทืกืงืก

ืœื•ื™ืฃ "ืคืึทื ื“ืึทืžืขื ื˜ืึทืœื– ืคื•ืŸ ืขืคืขืงื˜ื™ื•ื• ืึทืจื‘ืขื˜ ืžื™ื˜ Wolfram ื˜ืขืงื ืึทืœืึทื“ื–ืฉื™ื–": ืžืขืจ ื•ื•ื™ 13 ืฉืขื” ืคื•ืŸ ื•ื•ื™ื“ืขื ืจืขืคึฟืขืจืึทื˜ืŸ, ื˜ืขืึธืจื™ืข ืื•ืŸ ื˜ืึทืกืงืก

ืœื•ื™ืฃ "ืคืึทื ื“ืึทืžืขื ื˜ืึทืœื– ืคื•ืŸ ืขืคืขืงื˜ื™ื•ื• ืึทืจื‘ืขื˜ ืžื™ื˜ Wolfram ื˜ืขืงื ืึทืœืึทื“ื–ืฉื™ื–": ืžืขืจ ื•ื•ื™ 13 ืฉืขื” ืคื•ืŸ ื•ื•ื™ื“ืขื ืจืขืคึฟืขืจืึทื˜ืŸ, ื˜ืขืึธืจื™ืข ืื•ืŸ ื˜ืึทืกืงืก

ื›ืœ ืงื•ืจืก ื“ืึธืงื•ืžืขื ื˜ืŸ ืงืขื ืขืŸ ื–ื™ื™ืŸ ื“ืึทื•ื ืœืึธื•ื“ื™ื“ ื“ืึธ.

ืื™ืš ื’ืขืœืขืจื ื˜ ื“ืขื ืงื•ืจืก ืžื™ื˜ ืึท ืคึผืึธืจ ืคื•ืŸ ื™ืึธืจืŸ ืฆื•ืจื™ืง ืฆื• ืึท ื’ืึทื ืฅ ื’ืจื•ื™ืก ื•ื™ืœืขื. ืขืก ื›ึผื•ืœืœ ืึท ืคึผืœืึทืฅ ืคื•ืŸ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ื•ื•ืขื’ืŸ ื•ื•ื™ ื“ื™ ืกื™ืกื˜ืขื ืึทืจื‘ืขื˜ Mathematica, ื•ื•ืึธืœืคืจืึทื ืงืœืึธื•ื“ ืื•ืŸ ืฉืคึผืจืึทืš ื•ื•ืึธืœืคืจืึทื ืฉืคึผืจืึทืš.

ืึธื‘ืขืจ, ืคึฟืึทืจืฉื˜ื™ื™ื˜ ื–ื™ืš, ื“ื™ ืฆืฒึทื˜ ืฉื˜ื™ื™ื˜ ื ื™ืฉื˜ ืฉื˜ื™ืœ ืื•ืŸ ืึท ืกืš ื ืฒึทืข ื–ืึทื›ืŸ ื”ืึธื‘ืŸ ื–ื™ืš ืœืขืฆื˜ื ืก ื“ืขืจืฉื™ื ืขืŸ: ืคึฟื•ืŸ ืึทื•ื•ืึทื ืกื™ืจื˜ืข ืคึฟืขื™ึดืงื™ื™ื˜ืŸ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื ืขื•ืจืึทืœ ื ืขื˜ื•ื•ืึธืจืงืก ืฆื• ืึทืœืข ืžื™ื ื™ื ื•ื•ืขื‘ ืึทืคึผืขืจื™ื™ืฉืึทื ื–; ืื™ืฆื˜ ืขืก ืื™ื– ื•ื•ืึธืœืคืจืึทื ืขื ื’ื™ื ืข, ื•ื•ืึธืก ืื™ืจ ืงืขื ืขืŸ ื™ื ืกื˜ืึทืœื™ืจืŸ ืื•ื™ืฃ ื“ื™ื™ืŸ ืกืขืจื•ื•ืขืจ ืื•ืŸ ืึทืงืกืขืก ืขืก ื•ื•ื™ ืคึผื™ื˜ื”ืึธืŸ; ืื™ืจ ืงืขื ืขืŸ ื‘ื•ื™ืขืŸ ืึทืœืข ืžื™ื ื™ื ื“ื–ืฉื™ืึทื’ืจืึทืคื™ืง ื•ื•ื™ื–ืฉื•ื•ืึทืœืึทื–ื™ื™ืฉืึทืŸ ืึธื“ืขืจ ื›ืขืžื™ืฉืขืจ; ืขืก ื–ืขื ืขืŸ ืจื™ื–ื™ืง ืจื™ืคึผืึทื–ืึทื˜ืึธืจื™ื– ืึทืœืข ืžื™ื ื™ื ืคื•ืŸ ื“ืึทื˜ืŸ, ืึทืจื™ื™ึทื ื’ืขืจืขื›ื ื˜ ืžืึทืฉื™ืŸ ืœืขืจื ืขืŸ; ืื™ืจ ืงืขื ืขืŸ ืคืึทืจื‘ื™ื ื“ืŸ ืฆื• ืึทืœืข ืžื™ื ื™ื ืคื•ืŸ ื“ืึทื˜ืึทื‘ื™ื™ืกื™ื–; ืกืึธืœื•ื•ืข ืงืึธืžืคึผืœืขืงืก ืžืึทื˜ืึทืžืึทื˜ื™ืงืึทืœ ืคึผืจืึธื‘ืœืขืžืก, ืืื–"ื• ื•.

ืขืก ืื™ื– ืฉื•ื•ืขืจ ืฆื• ืจืฉื™ืžื” ืึทืœืข ื“ื™ ืงื™ื™ืคึผืึทื‘ื™ืœืึทื˜ื™ื– ืคื•ืŸ Wolfram ื˜ืขืงื ืึทืœืึทื“ื–ืฉื™ื– ืื™ืŸ ืึท ืคึผืึธืจ ืคื•ืŸ ืคึผืึทืจืึทื’ืจืึทืคืก ืึธื“ืขืจ ืึท ื‘ื™ืกืœ ืžื™ื ื•ื˜.

ื“ืึธืก ืึทืœืฅ ื”ืึธื˜ ืžื™ืš ื“ืขืจืžื•ื˜ื™ืงื˜ ืฆื• ื ืขืžืขืŸ ืึท ื ืฒึทืขื ืงื•ืจืก, ื•ื•ืึธืก ืื™ืš ื‘ื™ืŸ ืื™ืฆื˜ ืื•ื™ืฃ ืจืขื’ื™ืกื˜ืจืึทืฆื™ืข ืื™ืŸ ืคึผืจืึธื’ืจืขืก.

ืื™ืš ื‘ื™ืŸ ื–ื™ื›ืขืจ ืึทื– ืึทืžืึธืœ ืื™ืจ ืึทื ื˜ื“ืขืงืŸ ื“ื™ ืงื™ื™ืคึผืึทื‘ื™ืœืึทื˜ื™ื– ืคื•ืŸ ื“ื™ Wolfram ืฉืคึผืจืึทืš, ืื™ืจ ื•ื•ืขื˜ ืึธื ื”ื™ื™ื‘ืŸ ืฆื• ื ื•ืฆืŸ ืขืก ืžืขืจ ืื•ืŸ ืžืขืจ ืึธืคื˜, ืกืึทืœื•ื•ื™ื ื’ ื“ื™ื™ืŸ ืคึผืจืึธื‘ืœืขืžืก ื’ืขืฉื•ื•ื™ื ื“ ืื•ืŸ ื™ืคื™ืฉืึทื ื˜ืœื™ ืื™ืŸ ืคืึทืจืฉื™ื“ืŸ ื’ืขื‘ื™ื˜ืŸ: ืคึฟื•ืŸ ื•ื•ื™ืกื ืฉืึทืคึฟื˜ ืฆื• ืคึผืœืึทืŸ ืึธื˜ืึทืžื™ื™ืฉืึทืŸ ืึธื“ืขืจ ื•ื•ืขื‘ื–ื™ื™ื˜ืœ ืคึผืึทืจืกื™ื ื’, ืคึฟื•ืŸ ื ืขื•ืจืึทืœ ื ืขื˜ื•ื•ืึธืจืงืก ืฆื• ื’ืขืžืขืœ ืคึผืจืึทืกืขืกื™ื ื’, ืคื•ืŸ ืžืึธืœืขืงื•ืœืึทืจ ื•ื•ื™ื–ืฉื•ื•ืึทืœืึทื–ื™ื™ืฉืึทืŸ ืฆื• ืงืึทื ืกื˜ืจืึทืงืฉืึทืŸ ืฉื˜ืึทืจืง ื™ื ื˜ืขืจืึทืงืฉืึทื ื–.

1 | ืื™ื‘ืขืจื‘ืœื™ืง ืคื•ืŸ Wolfram Mathematica ืื•ืŸ Wolfram Cloud


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขื•ื•ืึธืก ืื™ื– Wolfram Mathematica?
โ€” ื‘ืืฉืขืคืขืจ โ€” ืกื˜ืขืคืืŸ ืฐืืœืคืจืื
โ€”โ€” ืขื˜ืœืขื›ืข ืคืจื™ืฉืข ืืจื˜ื™ืงืœืขืŸ ืคื•ืŸ ืกื˜ืขืคืืŸ ืฐืืœืคืจืื ืื™ื‘ืขืจื’ืขื–ืขืฆื˜ ืื•ื™ืฃ ืจื•ืกื™ืฉ
- ืจืฉื™ืžื” ืคื•ืŸ ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ืคืึทื ื’ืงืฉืึทื ื– ืื•ืŸ ืกื™ืžื‘ืึธืœืก
โ€”โ€” ื ื•ืžืขืจ ืคื•ืŸ ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ืคืึทื ื’ืงืฉืึทื ื– ื“ื™ืคึผืขื ื“ื™ื ื’ ืื•ื™ืฃ ื•ื•ืขืจืกื™ืข
โ€”โ€” ืคึผืœืึทืฅ ืื•ื™ืฃ ืฉื•ื•ืขืจ ื“ื™ืกืง
โ€” ืžืขืจ ืฐืขื’ืŸ ืžืื˜ืขืžืื˜ื™ืง ื‘ื›ืœืœ
- ืึทืœืข Wolfram ืคืึธืจืฉื•ื ื’ ืคึผืจืึธื“ื•ืงื˜ืŸ
ื ื™ื• ืื•ืŸ ื“ืขืจื”ื™ื™ึทื ื˜ื™ืงื˜ ืคึฟืขื™ึดืงื™ื™ื˜ืŸ
โ€” ืงืื“ ืฆื• ืงืจื™ื’ืŸ ื“ื™ ื“ืื–ื™ืงืข ืจืฉื™ืžื•ืช
ื ื™ื™ึท ืื™ืŸ ื“ื™ ืคืจืึธื ื˜ ืกื•ืฃ
ื ื™ื• ื“ื–ืฉื™ืึทืžืขื˜ืจื™ืง ืฉืคึผืจืึทืš
- ื™ืงืขืจื“ื™ืง ื“ื–ืฉื™ืึทืžืขื˜ืจื™ืง ืึทื‘ื“ื–ืฉืขืงืฅ
- ืคืึทื ื’ืงืฉืึทื ื– ืคึฟืึทืจ ื“ื–ืฉื™ืึทืžืขื˜ืจื™ืง ื—ืฉื‘ื•ื ื•ืช
โ€”โ€” ืฉื˜ื— ืžืึธืก
โ€”โ€” ืฐืฒื˜ ืฆื• ื’ืขื’ื ื˜
โ€”โ€” ืืจื‘ืขื˜ืŸ ืžื™ื˜ ืฉื˜ื—ื™ื
- ืคืึทื ื’ืงืฉืึทื ื– ืคึฟืึทืจ ื“ื™ืคื™ื™ื ื™ื ื’ ื’ืขื‘ื™ื˜ืŸ
โ€” ืืจื‘ืขื˜ืŸ ืžื™ื˜ ืžืขืฉื™ื
- ื’ืึทื ืฅ ื™ื ืึทื’ืจื™ื™ืฉืึทืŸ ืžื™ื˜ ืื ื“ืขืจืข ืคืึทื ื’ืงืฉืึทื ื–
ืึทื ืึทืœื™ื˜ื™ืฉ ืื•ืŸ ื ื•ืžืขืจื™ืงืึทืœ ืœื™ื™ื–ื•ื ื’ ืคื•ืŸ ื“ื™ืคืขืจืขื ื˜ืฉืึทืœ ื™ืงื•ื•ื™ื™ื–ืฉืึทื ื–
- ื•ื•ืขืŸ ืขื•ื•ืขื ื˜ ืคึฟืึทืจ ืึทื ืึทืœื™ื˜ื™ืงืึทืœ ื˜ืึทืกืงืก
- ืึทื ืึทืœื™ื˜ื™ืฉ ืœื™ื™ื–ื•ื ื’ ืคื•ืŸ ื“ืข ืžื™ื˜ ืคืึทืจื”ืึทืœื˜ืŸ
- ืขื ื“ืœืขืš ืขืœืขืžืขื ื˜ ืื•ืคึฟืŸ
ืžืึทืฉื™ืŸ ืœืขืจื ืขืŸ
- ืงืœืึทืกื™ืคื™ืฆื™ืจืŸ
- ืคืึธืจื•ื™ืกื–ืึธื’ืŸ
- ื‘ื™ื™ึทืฉืคึผื™ืœ
"ืฉืคึผืจืึทืš ืขื ื˜ื™ื˜ื™" - ืึท ื ื™ื™ึทืข ืฉืคึผืจืึทืš ืคึฟืึทืจ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื“ืึทื˜ืึทื‘ื™ื™ืกื™ื– + ื ืจื™ื–ื™ืง ื ื•ืžืขืจ ืคื•ืŸ ื ื™ื™ึทืข ื“ืึทื˜ืึทื‘ื™ื™ืกื™ื–
ื ื ื™ื™ึทืข ืฉืคึผืจืึทืš ืคึฟืึทืจ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื“ื–ืฉื™ืึทื’ืจืึทืคื™ืง ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข
ื•ื•ืึธืก ื–ืขื ืขืŸ ืื ื“ืขืจืข ื ื™ื™ึทืขืก?
โ€” ืคืืจืœืขื ื’ืขืจื•ื ื’ ืคื•ืŸ ื“ืขืจ ื‘ืื–ืข ืฉืคืจืืš
- ืคืึทืจื‘ืึทื ื“ - ื™ื ื“ืขืงืกื˜ ืขืจื™ื™ื–
- ื“ืึทื˜ืึทืกืขื˜ - ืึท ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ื“ื™ื™ื˜ืึทื‘ื™ื™ืก ืคึฟืึธืจืžืึทื˜
- ืคึผืœืึทื˜ื˜ื”ืขืžืข
โ€” ืฆืฒื˜ึพืฉืฒื ื“ืข ื—ืฉื‘ื•ื ื•ืช
- ืึทื ืึทืœื™ืกื™ืก ืคื•ืŸ ื˜ืจืึทืค - ืคึผืจืึทืกืขืกืึทื–
โ€” ืฆื™ื™ื˜ึพืกืขืจื™ืข
- ื™ื ืึทื’ืจื™ื™ืฉืึทืŸ ืžื™ื˜ Wolfram Cloud
- ื™ื ืึทื’ืจื™ื™ืฉืึทืŸ ืžื™ื˜ ื“ื™ื•ื•ื™ื™ืกืึทื–
- ืึทื•ื•ืึทื ืกื™ืจื˜ืข ื“ืึธืงื•ืžืขื ื˜ ื˜ืขืžืคึผืœืึทื˜ืขืก, HTML
ื•ื•ืึธืœืคืจืึทื ืคึผืจืึธื’ืจืึทืžืžื™ื ื’ ืงืœืึธื•ื“

2.1 | ื”ืงื“ืžื” ืฆื• ื“ืขืจ ืฉืคึผืจืึทืš, ืื™ืจ ืคึฟืขื™ึดืงื™ื™ื˜ืŸ. ื“ื™ ื”ื•ื™ืคึผื˜ ืฉื•ื•ืขืจื™ืงื™ื™ื˜ืŸ ืคึฟืึทืจ ืึธื ื”ื™ื™ื‘ืขืจ ื ื™ืฆืขืจืก. ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื“ื™ Mathematica ืฆื•ื‘ื™ื ื“ ืื•ืŸ ื–ื™ื™ึทืŸ ืงื™ื™ืคึผืึทื‘ื™ืœืึทื˜ื™ื– - ืคึผืจื™ื“ื™ืงื˜ื™ื•ื• ืฆื•ื‘ื™ื ื“, ืคืจื™ื™ ืึทืจื™ื™ึทื ืฉืจื™ื™ึทื‘ ืคืึธืจืขื, ืขื˜ืง.


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขื•ื•ืึธืœืคืจืึทื ืฉืคึผืจืึทืš
ื•ื•ืึธืœืคืจืึทื ืฉืคึผืจืึทืš ืคึผืจื™ื ืกืึทืคึผืึทืœื–
ื•ื•ืึธืก ืื™ื– ื•ื•ื™ื›ื˜ื™ืง ืฆื• ื’ืขื“ืขื ืงืขืŸ ื•ื•ืขืŸ ืื™ืจ ืึทืจื‘ืขื˜ ืžื™ื˜ Wolfram ืฉืคึผืจืึทืš?
ืึธื ื”ื™ื™ื‘ ืื™ืŸ ืžืึทื˜ื”ืขืžืึทื˜ื™ืงืึท
ื•ื•ื™ื›ื˜ื™ืง ืงืœืึทื•ื•ื™ืึทื˜ื•ืจ ืฉืึธืจื˜ืงืึทืฅ
- ืฉื™ืคื˜ + ืึทืจื™ื™ึทืŸ ืึธื“ืขืจ ืึทืจื™ื™ึทืŸ ืื•ื™ืฃ ื“ื™ ื ื•ืžืขืจื™ืง ืงื™ืคึผืึทื“
- ืงื˜ืจืœ + ืฉื™ืคื˜ + ืึทืจื™ื™ึทืŸ
- F1
- F2
ื‘ืึทืงื•ืžืขืŸ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ื•ื•ืขื’ืŸ ืกื™ืžื‘ืึธืœืก
โ€”? - ืคึฟื•ื ืงืฆื™ืข ื“ืขืคื™ื ื™ืฆื™ืข
- ?? - ืคึฟื•ื ืงืฆื™ืข ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข
- ื“ืจื™ืงื˜ ืื•ื™ืฃ F1
- ืคึผืจื™ื“ื™ืงื˜ื™ื•ื• ืฆื•ื‘ื™ื ื“
ืึทืจื‘ืขื˜ ืžื™ื˜ ืคึผืึทืœืขื˜ื˜ืขืก
- ื™ืงืขืจื“ื™ืง ืžืึทื˜ ืึทืกืกื™ืกื˜ืึทื ื˜
โ€” ืงืœืึทืกืฆื™ืžืขืจ ืึทืกืกื™ืกื˜ืึทื ื˜
โ€” ืฉืจื™ื™ื‘ืขืจึพืืกื™ืกื˜ืขื ื˜
- ื˜ืฉืึทืจื˜ ืขืœืขืžืขื ื˜ ืกื˜ืฉืขืžืขืก
โ€” ืงืืœื™ืจ ืกืงื™ืžื–
โ€” ืกืคืขืฆื™ืขืœืข ื›ืืจืืงื˜ืขืจืŸ
- ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื’ืจืึทืคืก ืื•ืŸ ื“ืจืึทื•ื•ื™ื ื’ืก
โ€”โ€” ืฆื™ื™ื›ืขื ื•ื ื’ ืžื›ืฉื™ืจื™ื
โ€”โ€”ื‘ืึทืงื•ืžืขืŸ ืงืึธืึธืจื“ื™ื ืึทื˜ืขืก
โ€”โ€” ืขืจืฉื˜ื™ืง ื‘ื™ืœื“ ืคึผืจืึทืกืขืกื™ื ื’
โ€” ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื’ืจืึทืคืก
ื•ื•ืึธืœืคืจืึทื ืฉืคึผืจืึทืš & ืกื™ืกื˜ืขื | ื“ืึทืงื™ื•ืžืขื ื˜ื™ื™ืฉืึทืŸ ืฆืขื ื˜ืขืจ
ืคึผืจื™ื“ื™ืงื˜ื™ื•ื• ืฆื•ื‘ื™ื ื“
- ืงืึธื ื˜ืขืงืกื˜-ืฉืคึผื™ืจืขื•ื•ื“ื™ืง ืึทื•ื˜ืึธืงืึธืžืคึผืœืขื˜ื™ืึธืŸ ืคื•ืŸ ืืจื™ื™ืŸ ืงืึทืžืึทื ื“ื–
โ€”โ€” ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ืคืึทื ื’ืงืฉืึทื ื– ืื•ืŸ ืกื™ื ื˜ืึทืงืก ืคึผืึทื˜ืขืจื ื–
โ€”โ€” ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื‘ืึทื ื™ืฆืขืจ ื•ื•ืขืจื™ืึทื‘ืึทืœื–
- ืงืึทืœืงื™ืึทืœื™ื™ื˜ื™ื“ ืคึผืจื™ื“ื™ืงื˜ื™ื•ื• ืฆื•ื‘ื™ื ื“ - ื˜ืึทืคืœื™ืข ืคึฟืึทืจ ืกืึทื’ื“ื–ืฉืขืกื˜ื™ื ื’ ื•ื•ื™ื™ึทื˜ืขืจ ืึทืงืฉืึทื ื–
ื™ื ื˜ืขื’ืจืึทื˜ื™ืึธืŸ ืžื™ื˜ Wolfram|Alpha
โ€” Wolfram|Alpha ื•ื•ืขื‘ื–ื™ื™ื˜ืœ
- ื™ื ืึทื’ืจื™ื™ืฉืึทืŸ ืฆื•ื•ื™ืฉืŸ ื•ื•ืึธืœืคืจืึทื|ืึทืœืฃ ืื•ืŸ ืžืึทื˜ื”ืขืžืึทื˜ื™ืงืึท
โ€”โ€” ื’ืขืคื™ื ืข ืŸ ืคืืจืžืื›ื˜ืข ืจ ืคืืจืฉื˜ืขืœื•ื  ื’ ืคื• ืŸ ื“ืขืฆื™ืžืืœืข ืจ ืคืจืืงืฆื™ืขืก
โ€”โ€” ื‘ืœื•ื˜ื“ืจื•ืง ืื™ื ืคืืจืžืืฆื™ืข
โ€”โ€” ืฉืจื™ื˜-ื“ื•ืจืš-ืฉืจื™ื˜ ืœื™ื™ื–ื•ื ื’ ืคื•ืŸ ืึท ืžืึทื˜ืจื™ืฅ ื™ืงื•ื•ื™ื™ื–ืฉืึทืŸ ื ื™ืฆืŸ ื“ื™ ื’ืึทื•ืกื™ืึทืŸ ืื•ืคึฟืŸ

2.2 | ืกืคึผืขืฆื™ืคื™ืฆื™ืจืŸ ืคืึทื ื’ืงืฉืึทื ื–, ืืจื‘ืขื˜ืŸ ืžื™ื˜ ืจืฉื™ืžื•ืช, ืžื•ืกื˜ืขืจ ืื•ื™ืกื“ืจื•ืงืŸ ืื•ืŸ ืึทืกืึธื•ืกื™ื™ื™ืฉืึทื ื–


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขืจืฉื™ืžื•ืช
โ€” ืจืฉื™ืžื” {...} ืื•ืŸ ืคึฟื•ื ืงืฆื™ืข ืจืขืฉื™ืžืข[โ€ฆ] - "ื ืึทื˜ื™ืจืœืขืš" ืึทืจื•ื™ืกื•ื•ื™ื™ึทื–ืŸ ืคื•ืŸ ืจืฉื™ืžื•ืช
- ื•ื•ืขื’ืŸ ืฆื• ื“ื–ืฉืขื ืขืจื™ื™ื˜ ืจืฉื™ืžื•ืช
- ื™ื ื“ืขืงืกื™ื ื’ ืคื•ืŸ ืขืœืขืžืขื ื˜ืŸ ืื•ืŸ ืขื˜ืœืขื›ืข ื ื•ืžืขืจื™ืงืึทืœ ืงืขืจืึทืงื˜ืขืจื™ืกื˜ื™ืงืก ืคื•ืŸ ื“ืขืจ ืจืฉื™ืžื”. ืคืึทื ื’ืงืฉืึทื ื– ืœืขื ื’ ะธ ื˜ื™ืฃ
- ืกืขืœืขืงื˜ื™ื ื’ ืขืœืขืžืขื ื˜ืŸ ื•ื•ืึธืก ืคืึทืจื ืขืžืขืŸ ื–ื™ื›ืขืจ ืขืจื˜ืขืจ ืื™ืŸ ื“ืขืจ ืจืฉื™ืžื” ื ื™ืฆืŸ ื“ื™ ืคึฟื•ื ืงืฆื™ืข ื˜ื™ื™ืœ([[...]])
- ืจื™ื ื™ื™ืžื™ื ื’ ืจืฉื™ืžื” ื–ืื›ืŸ
- ื“ื–ืฉืขื ืขืจื™ื™ื˜ื™ื ื’ ืึท ืจืฉื™ืžื” ืžื™ื˜ ื“ื™ ืคึฟื•ื ืงืฆื™ืข ื˜ื™ืฉ
- ื“ื–ืฉืขื ืขืจื™ื™ื˜ื™ื ื’ ืึท ืจืฉื™ืžื” ืคื•ืŸ ื ื•ืžืขืจืŸ ื ื™ืฆืŸ ืึท ืคึฟื•ื ืงืฆื™ืข ืงื™ื™ื˜
ืึทืกืึธื•ืกื™ื™ื™ืฉืึทื ื–
โ€” ืื•ื™ืคืฉื˜ืขืœืŸ ื ืคืืจื‘ืื ื“ ืื•ืŸ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ืื™ื
- ื“ืึทื˜ืึทืกืขื˜ - ื“ืึทื˜ืึทื‘ื™ื™ืก ืคึฟืึธืจืžืึทื˜ ืื™ืŸ ื“ื™ Wolfram ืฉืคึผืจืึทืš
ืžื•ืกื˜ืขืจ ืขืงืกืคึผืจืขืกืกื™ืึธื ืก
- ื”ืงื“ืžื” ืฆื• ื˜ืขืžืคึผืœืึทื˜ืขืก
- ื™ืงืขืจื“ื™ืง ืึทื‘ื“ื–ืฉืขืงืฅ ื˜ืขืžืคึผืœืึทื˜ืขืก: Blank (_), BlankSequence (__), BlankNullSequence (___)
โ€” ื•ื•ืึธืก ืงืขื ืขืŸ ืื™ืจ ื˜ืึธืŸ ืžื™ื˜ ื˜ืขืžืคึผืœืึทื˜ืขืก? ืคึฟื•ื ืงืฆื™ืข ืงืึทืกืขืก
- ื‘ืึทืฉื˜ื™ืžืขืŸ ื“ืขื ื˜ื™ืคึผ ืคื•ืŸ ืื•ื™ืกื“ืจื•ืง ืื™ืŸ ื“ื™ ืžื•ืกื˜ืขืจ
- ื™ืžืคึผืึธื•ื–ื™ื ื’ ืจื™ืกื˜ืจื™ืงืฉืึทื ื– ืื•ื™ืฃ ื˜ืขืžืคึผืœืึทื˜ืขืก ื ื™ืฆืŸ ืคืึทื ื’ืงืฉืึทื ื– ืฆื•ืฉื˜ืึทื ื“ (/;), ืžื•ืกื˜ืขืจ ื˜ืขืกื˜ (?), ื•ื™ืกืขืจ, ื•ื•ื™ ื’ืขื–ื•ื ื˜ ื•ื•ื™ ื“ื™ ื ื•ืฆืŸ ืคื•ืŸ ืคึผืจื•ื‘ื™ืจืŸ ืคืึทื ื’ืงืฉืึทื ื–
- ืฉืึทืคื•ื ื’ ืคื•ืŸ ื˜ืขืžืคึผืœืึทื˜ืขืก ืžื™ื˜ ื“ื™ ืžืขื’ืœืขื›ืงื™ื™ื˜ ืคื•ืŸ ืึธืœื˜ืขืจื ืึทื˜ื™ื•ื• ืกืขืœืขืงืฆื™ืข ื ื™ืฆืŸ ื“ื™ ืคื•ื ืงืฆื™ืข ืึทืœื˜ืขืจื ืึทื˜ื™ื•ื•ืขืก (|)
ืคืึทื ื’ืงืฉืึทื ื–
- ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ ืคื•ืŸ ื“ื™ืคืขืจื“ ืึทืกื™ื™ื ืžืึทื ื˜ SetDelayed (:=)
- ื ื™ืฆืŸ ืึทื‘ืกืึธืœื•ื˜ ืึทืกื™ื™ื ืžืึทื ื˜ ืฉื˜ืขืœืŸ (=)
- ื‘ืึทืฉื˜ืขื˜ื™ืงืŸ ืึท ืคื•ื ืงืฆื™ืข ื•ื•ืึธืก ื’ืขื“ืขื ืงื˜ ื“ื™ ื•ื•ืึทืœื•ืขืก ื•ื•ืึธืก ืขืก ื”ืื˜ ืฉื•ื™ืŸ ื’ืขืคึฟื•ื ืขืŸ ืื•ืŸ ืึท ืจื™ืงืขืจืึทื ื˜ ืคื•ื ืงืฆื™ืข
- ืคื•ื ืงืฆื™ืข ืึทื˜ืจื™ื‘ื™ื•ืฅ ืื•ืŸ ืคืึทื ื’ืงืฉืึทื ื– ืึทื˜ืจืึทื‘ื™ื•ืฅ, SetAttributes, ืงืœืึธืจ ืึทื˜ืจื™ื‘ื™ื•ืฅ, ื‘ืึทืฉื™ืฆืŸ, ืึทื ืคึผืจืึทื˜ืขืงื˜ื™ื“ ืฆื• ืึทืจื‘ืขื˜ืŸ ืžื™ื˜ ื–ื™ื™
ืจื™ื™ืŸ ืคืึทื ื’ืงืฉืึทื ื–
- ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ ืคื•ืŸ ื“ื™ ืคึฟื•ื ืงืฆื™ืข ืคื•ื ืงืฆื™ืข (&)
โ€” ืฐืื• ืฐืขืจืŸ ื’ืขื ื•ืฆื˜ ืจื™ื™ื ืข ืคื•ื ืงืฆื™ืขืก?

2.3 | ืฉืืคืŸ ื•ื•ื™ื–ืฉื•ื•ืึทืœืึทื–ื™ื™ืฉืึทื ื–


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขืกื™ืžื‘ืึธืœื™ืฉ ื’ืจืึทืคื™ืง ืฉืคึผืจืึทืš
โ€” ื’ืจืืคื™ืฉืข ืคืจื™ืžื™ื˜ื™ื•ื•ืŸ
โ€”โ€” ืืฒืŸึพื“ื™ืžืขื ืฉืึทื ืึทืœ
โ€”โ€” ืฆืฐืฒึพื“ื™ืžืขื ืฉืึทื ืึทืœ
โ€”โ€” ื“ืจืฒึพื“ื™ืžืขื ืฉืึทื ืึทืœ
โ€”โ€” ื”ื™ืœืฃ
- ืคึฟื•ื ืงืฆื™ืข ื’ืจืึทืคื™ืงืก
โ€”โ€” ืกื™ื ื˜ืืงืก
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
โ€”โ€”โ€” ืฉื™ื›ื˜ืŸ
โ€”โ€”โ€” ืฉื™ื›ื˜ืข ืจื™ืืจืื ื–ืฉื™ืจืŸ
โ€”โ€”โ€” ืืœื’ืขืžื™ื™ื ืข ืื•ืŸ ืกืคืขืฆื™ืคื™ืฉืข ืื™ื™ื’ื ืฉืืคื˜ืŸ ืคื•ืŸ ืฉื™ื›ื˜ืŸ
โ€”โ€” ืคึฟื•ื ืงืฆื™ืข ืึธืคึผืฆื™ืขืก ื’ืจืึทืคื™ืงืก
--- AspectRatio
--- ืึทืงืกืขืก
--- AxesLabel
--- AxesOrigin
--- AxesStyle
--- ื˜ื™ืงืก
--- ื˜ื™ืงืก ืกื˜ื™ืœ
--- ื”ื™ื ื˜ืขืจื’ืจื•ื ื˜
--- ืื™ื ื”ืึทืœื˜ ืกืขืœืขืงื˜ืึทื‘ืœืข
--- ืงืึธืึธืจื“ื™ื ืึทื˜ืขืก ืžื›ืฉื™ืจื™ื
--- ืขืคึผื™ืœืึธื’
--- ืคึผืจืึธืœืึธื’
--- ืจืึทื
--- FrameLabel
--- RotateLabel
--- FrameStyle
--- FrameTicks
--- FrameTicksStyle
--- ื’ืจื™ื“ืœื™ื ืขืก
--- GridLinesStyle
--- ื‘ื™ืœื“ ื’ืจื™ื™ืก
--- ืคึผืœืึทื˜ืœืึทื‘ืขืœ
--- LabelStyle
--- PlotRange
--- PlotRangeClipping
--- PlotRangePadding
โ€”โ€” ืกื˜ื™ืœ ืกืขื˜ื˜ื™ื ื’ืก
โ€”โ€”โ€” ืงืึธืœืึธืจืก (ื’ืขื”ื™ื™ืกืŸ ืคืืจื‘ืŸ + ืคืืจื‘ืŸ ืคึฟื•ืŸ ืงืึธืœื™ืจ ืกืคึผื™ื™ืกืึทื–, ื–ืึธื’ืŸ RGBColor), ื“ื•ืจื›ื–ืขื™ืงื™ื™ึทื˜ (Opacity)
โ€”โ€”โ€” ืฉื•ืจื” ื’ืจืขื‘: ื“ื™ืง, ื“ื™ืŸ, ื’ืจืขื‘, ืึทื‘ืกืึธืœื•ื˜ ื’ืจืขื‘
โ€”โ€”โ€” ืคึผื•ื ืงื˜ ื’ืจื™ื™ืก: PointSize, AbsolutePointSize
โ€”โ€”โ€” ื ื•ืกื— ืคื•ืŸ ืกืึธืฃ ืฉื•ืจื•ืช ืื•ืŸ ื‘ืจืขื›ืŸ ืคื•ื ืงื˜ืŸ: ืงืึทืคึผืคืึธืจื, ืคืึทืจื‘ื™ื ื“ืŸ ืคืึธืจื
โ€”โ€”โ€” ืคึฟื•ื ืงืฆื™ืข ืกื˜ื™ืœ ืฆื• ืงืึทืกื˜ืึทืžื™ื™ื– ื“ื™ ืื•ื™ืกื–ืขืŸ ืคื•ืŸ ื˜ืขืงืกื˜
โ€”โ€”โ€” ืคืึทื ื’ืงืฉืึทื ื– FaceForm ะธ ืขื“ื–ืฉืคืึธืจื ืฆื• ืงืึธื ื˜ืจืึธืœื™ืจืŸ ื“ื™ ืื•ื™ืกื–ืขืŸ ืคื•ืŸ ืึท ื’ืขื’ื ื˜ ืื•ืŸ ื–ื™ื™ึทืŸ ื’ืขืžืืจืงืŸ
-- ื‘ื™ื™ึทืฉืคึผื™ืœ
โ€”โ€”โ€” ื“ืขืจื ืขื ื˜ืขืจืŸ ืœื™ื™ื–ื•ื ื’
โ€”โ€”โ€” ื“ื™ ืœื™ื™ื–ื•ื ื’ ืื™ื– ื’ืขื ื•ื™
โ€”โ€”โ€” ืคืืจืฐืื ืื™ื– ื“ื™ ื’ืขื ื•ื™ืข ืœืฒื–ื•ื ื’ ื–ืฒืขืจ ื ื•ืฆืœื™ืš?
- ืคึฟื•ื ืงืฆื™ืข ื’ืจืึทืคื™ืงืก 3 ื“
โ€”โ€” ืกื™ื ื˜ืืงืก
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
โ€”โ€”โ€” ืึทืœื’ืขืžื™ื™ื ืข ืื•ืŸ ืกืคึผืขืฆื™ืคื™ืฉ ืคึผืจืึธืคึผืขืจื˜ื™ืขืก ืคื•ืŸ ื’ืจืึทืคื™ืง ืึทื‘ื“ื–ืฉืขืงืฅ
โ€”โ€” ืคึฟื•ื ืงืฆื™ืข ืึธืคึผืฆื™ืขืก ื’ืจืึทืคื™ืงืก 3 ื“
--- AxesEdge
--- ื‘ืึธืงืกืขื“
--- BoxRatios
--- BoxStyle
--- ืงืœื™ืคึผ ืคึผืœืึทื ืขืก
--- ClipPlanesStyle
--- FaceGrids
--- FaceGridsStyle
--- ืœื™ื’ื”ื˜ื™ื ื’
--- ืกืคืขืจื™ืฉ ื’ืขื’ื ื˜
--- ื•ื•ื™ืขื•ื•ืคึผืึธื™ื ื˜, ViewVector, ViewVertical
โ€”โ€” ื‘ื™ื™ืฉืคึผื™ืœ: ืึท ืงืจื™ื™ึทื– ืึธืคึผื˜ื™ื™ืœื•ื ื’ ืคื•ืŸ ืึท ืงื•ื‘
โ€”โ€”โ€” ืคื•ืŸ ืึท ืกื˜ืึทื˜ื™ืง ื“ืจื™ื™-ื“ื™ืžืขื ืฉืึทื ืึทืœ ื›ื™ื™ืคืขืฅ ืฆื• ืึทืŸ ื™ื ื˜ืขืจืึทืงื˜ื™ื•ื•ืข
ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ืคืึทื ื’ืงืฉืึทื ื– ืคึฟืึทืจ ืงืจื™ื™ื™ื˜ื™ื ื’ ื•ื•ื™ื–ืฉื•ื•ืึทืœืึทื–ื™ื™ืฉืึทื ื–
ื™ืงืขืจื“ื™ืง 2 ื“ ืคืึทื ื’ืงืฉืึทื ื–
- ืคึผืœืึธื˜
- ืงืึธื ื˜ืึธื•ืจืคึผืœืึธื˜
- ืจืขื’ื™ืึธื ืึทืœ ืคึผืœืึทื˜
- ืคึผืึทืจืึทืžืขื˜ืจื™ืง ืคึผืœืึทื˜
- PolarPlot
- ืจืฉื™ืžื” ืคึผืœืึทื˜
ื™ืงืขืจื“ื™ืง 3 ื“ ืคืึทื ื’ืงืฉืึทื ื–
- ืคึผืœืึทื˜3ื“
- ืงืึธื ื˜ืึธื•ืจืคึผืœืึธื˜3ื“
- RegionPlot3D
- ParametricPlot3D
- ืจืฉื™ืžื” ืคึผืœืึทื˜3ื“
ืคึฟืึทืจื‘ื™ื ื“ื•ื ื’ ืคื•ืŸ ืคืึทื ื’ืงืฉืึทื ื– ืคึฟืึทืจ ื‘ื ื™ืŸ ื•ื•ื™ื–ืฉื•ื•ืึทืœืึทื–ื™ื™ืฉืึทื ื– ืื•ืŸ ื™ืงืขืจื“ื™ืง ืคืึทื ื’ืงืฉืึทื ื– ื’ืจืึทืคื™ืงืก ะธ ื’ืจืึทืคื™ืงืก 3 ื“
โ€” 2 ื“
โ€” 3 ื“

2.4 | ืงืจื™ื™ื™ื˜ื™ื ื’ ื™ื ื˜ืขืจืึทืงื˜ื™ื•ื• ืึทื‘ื“ื–ืฉืขืงืฅ, ืืจื‘ืขื˜ืŸ ืžื™ื˜ ืงืึธื ื˜ืจืึธืœืก, ืงืจื™ื™ื™ื˜ื™ื ื’ ื‘ืึทื ื™ืฆืขืจ ื™ื ื˜ืขืจืคื™ื™ืกื™ื–


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขืกื™ืžื‘ืึธืœื™ืฉ ื“ื™ื ืึทืžื™ืฉ ืฉืคึผืจืึทืš
- ืคึฟื•ื ืงืฆื™ืข ื“ื™ื ืึทืžื™ืฉ
โ€”โ€” ืคึผืฉื•ื˜ืข ื‘ื™ื™ืฉืคื™ืœืŸ
โ€”โ€”โ€” ื˜ื•ื™ืฉืŸ ืึท ืคึผืึทืจืึทืžืขื˜ืขืจ
โ€”โ€”โ€” ืœื™ื™ื–ื•ื ื’ ืงืึทื ืกื˜ืจืึทืงืฉืึทืŸ ืึทืจื•ื™ืกื•ื•ื™ื™ึทื–ืŸ
โ€” ืงืึธื ื˜ืจืึธืœืก
- ืกืœื™ื™ื“ืขืจ
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
- ืกืœื™ื™ื“ืขืจ2ื“
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
- ื™ื ื˜ืขืจื•ื•ืึทืœืกืœื™ื“ืขืจ
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
- ื˜ืฉืขืงืงื‘ืึธืงืก
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
- ื˜ืฉืขืงืงื‘ืึธืงืกื‘ืึทืจ
- ืกืขื˜ืขืจ
- SetterBar
- ืจืึทื“ื™ืึธ ืงื ืขืคึผืœ - ืกืคึผืขืฆื™ืขืœ ื˜ื™ืคึผ ืกืขื˜ืขืจ
- RadioButtonBar - ืกืคึผืขืฆื™ืขืœ ื˜ื™ืคึผ SetterBar
- ื˜ืึธื’ื’ืœืขืจ
- ToggleBar
- ืึธืคึผืขื ืขืจ
- ืงืึธืœืึธืจืกืœื™ื“ืขืจ
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
- PopupMenu
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
- InputField
โ€”โ€”โ€” ื“ืขืจ ืืฒื ืคืื›ืกื˜ืขืจ ื‘ืฒืฉืคื™ืขืœ
โ€”โ€” ืื ื“ืขืจืข ื—ืคืฆื™ื...
ืคื•ื ืงืฆื™ืึธื ื™ืจืŸ ืžืึทื ื™ืคึผื•ืœื™ืจืŸ
โ€” ืกื™ื ื˜ืืงืก
- ืกื™ืžืคึผืœืึทืคื™ื™ื“ ืกื™ื ื˜ืึทืงืก ืคื•ืŸ ืงืึธื ื˜ืจืึธืœืก
โ€”โ€” {ืจืขื ื˜ื’ืขื , ืึท, ื‘}
โ€”โ€” {ืจืขื ื˜ื’ืขื , ืึท, ื‘, ื“ืงืก}
โ€”- {{ืจืขื ื˜ื’ืขื , ืงืก0}, ืึท, ื‘}, {{ืจืขื ื˜ื’ืขื , ืงืก0}, ืึท, ื‘, ื“ืงืก}
โ€”- {{ืจืขื ื˜ื’ืขื , ืงืก0, ืคื™ืจืžืข}, ืึท, ื‘}, {{ืจืขื ื˜ื’ืขื , ืงืก0, ืคื™ืจืžืข}, ืึท, ื‘, ื“ืงืก}
โ€”โ€” {{ืจืขื ื˜ื’ืขื , ืขืจืฉื˜, ืคื™ืจืžืข}, โ€ฆ.}
โ€”โ€” {ืจืขื ื˜ื’ืขื , ืงืึธืœื™ืจ}
โ€”โ€” {ืจืขื ื˜ื’ืขื , {ื•ื•ืึทืœ1, ื•ื•ืึทืœ2, โ€ฆ}}
โ€”โ€” {ืจืขื ื˜ื’ืขื , {ื•ื•ืึทืœ1-ืœื‘ืœ1, ื•ื•ืึทืœ2->ืœื‘ืœ2, ...}}
โ€”โ€” {ืงืก, {ืงืกืžื™ืŸ, ื™ืžื™ืŸ}, {ืงืกืžืึทืงืก, ื™ืžืึทืงืก}}
โ€”โ€” {ืจืขื ื˜ื’ืขื , {ืืžืช, ืคืึทืœืฉ}}
โ€”โ€” {X} ืื•ืŸ {{X, X0}}
โ€”โ€” {ืจืขื ื˜ื’ืขื , ืœืึธืงืึทื˜ืึธืจ}
โ€”โ€” {ืงืก, {ืงืกืžื™ืŸ, ื™ืžื™ืŸ}, {ืงืกืžืึทืงืก, ื™ืžืึทืงืก}, ืœืึธืงืึทื˜ืึธืจ}
โ€”โ€” {{ืงืก, {{ืงืก1, ื™1}, {ืงืก2, ื™2}, ...}}, ืœืึธืงืึทื˜ืึธืจ} ืึธื“ืขืจ
{{ืงืก, {{ืงืก1, ื™1}, {ืงืก2, ื™2}, โ€ฆ}}, {ืงืกืžื™ืŸ, ื™ืžื™ืŸ}, {ืงืกืžืึทืงืก, ื™ืžืึทืงืก}, ืœืึธืงืึทื˜ืึธืจ}
โ€”โ€” {{ืจืขื ื˜ื’ืขื , โ€ฆ}, โ€ฆ, ืœืึธืงืึทื˜ืึธืจ, ืœืึธืงืึทื˜ืึธืจ ืึทื•ื˜ืึธืงืจืขืึทื˜ืข-> ืืžืช
โ€”โ€” {{ืจืขื ื˜ื’ืขื , โ€ฆ}, โ€ฆ, ื˜ื™ืคึผ}
โ€” ืึธืคึผืฆื™ืขืก ืžืึทื ื™ืคึผื•ืœื™ืจืŸ
- ืงืขืกื™ื™ื“ืขืจื“ื™ืง ืงืึทืžืฃ
- ืœืึธืงืึทืœื™ื–ืข ื•ื•ืึทืจื™ืึทื‘ืœืขืก
- ื™ื ื™ื˜ื™ืึทืœื™ื–ืึทื˜ื™ืึธืŸ
- SaveDefinitions
- ืกื™ื ื˜ืฉืจืึธื ืึธื•ืก ื™ื ื™ื˜ื™ืึทืœื™ื–ืึทื˜ื™ืึธืŸ
- ืกื™ื ื˜ืฉืจืึธื ืึธื•ืก ืึทืคึผื“ื™ื™ื˜ื™ื ื’
- TrackedSymbols
- ื“ื™ื–ื™ื™ื ืขืจ ืคื•ืŸ ืžืึทื ื™ืคึผื™ืึทืœื™ื™ื˜ืขืจื–
- ืงืจื™ื™ื™ื˜ื™ื ื’ ืœื™ื ื’ืงื˜ ืžืึทื ื™ืคึผื™ืึทืœื™ื™ื˜ืขืจื– ืื•ืŸ ืคึฟืึทืจื‘ื™ื ื“ื•ื ื’ ืœืึธืงืึทื˜ืึธืจืก ืฆื• ืึท ื•ื™ืกื‘ื™ื™ื’ ื ื™ืฆืŸ ื“ื™ ืึธืคึผืฆื™ืข ื˜ืจืึทืงื™ื ื’ืคื•ื ืงื˜ื™ืึธืŸ

2.5 | ืึทืจื™ื™ึทื ืคื™ืจ, ืึทืจื•ื™ืกืคื™ืจืŸ, ืคึผืจืึทืกืขืกื™ื ื’ ืคื•ืŸ ื“ืึทื˜ืŸ, ื˜ืขืงืขืก, ื‘ื™ืœื“ืขืจ, ื’ืขื–ื•ื ื˜, ื•ื•ืขื‘ ื–ื™ื™ึทื˜ืœืขืš. ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื“ื™ ืึทืคึผื™ ืคื•ืŸ ื•ื•ืขื‘ ืจืขืกื•ืจืกืŸ ืžื™ื˜ ื“ื™ ื‘ื™ื™ืฉืคึผื™ืœ ืคื•ืŸ ื“ื™ VKontakte API, ื•ื•ื™ ื’ืขื–ื•ื ื˜ ื•ื•ื™ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื“ื™ ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ืžืขื˜ื”ืึธื“ืก ืคื•ืŸ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื“ื™ ืึทืคึผื™ ืคื•ืŸ ืคืึทืกืขื‘ืึธืึธืง, ื˜ื•ื•ื™ื˜ื˜ืขืจ, ื™ื ืกื˜ืึทื’ืจืึทื, ืขื˜ืง.


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขืืจื‘ืขื˜ืŸ ืžื™ื˜ ื˜ืขืงืขืก ืื•ืŸ ื–ื™ื™ืขืจ ื ืขืžืขืŸ
- ื˜ืขืงืข ื–ื•ื›ืŸ ืื•ืŸ ืคึฟืึทืจื‘ื•ื ื“ืขื ืข ื˜ืึทืกืงืก
- $ ื™ื ืกื˜ืึทืœืœืึทื˜ื™ืึธืŸื“ื™ืจืขืงื˜ืึธืจื™, $BaseDirectory
- ื ืึธื•ื˜ื‘ื•ืงื“ื™ืจืขืงื˜ืึธืจื™
- FileExistsQ
- ืคื™ืœืขื ืึทืžืขืก
- ืงืจื™ื™ื™ื˜ื™ื ื’ ื˜ืขืงืข ื ืขืžืขืŸ
- DirectoryName
- FileNameJoin
- FileNameSplit
- FileNameTake
- FileBaseName
- FileExtension
ืคืึทื ื’ืงืฉืึทื ื– ืึทืจื™ื™ึทื ืคื™ืจ ะธ ืึทืจื•ื™ืกืคื™ืจืŸ
- ื™ืžืคึผืึธืจื˜ ืื•ืŸ ืึทืจื•ื™ืกืคื™ืจืŸ ืคึฟืึธืจืžืึทื˜ื™ืจื•ื ื’ืขืŸ
- ืึทืจื™ื™ึทื ืคื™ืจ
โ€”โ€” ื‘ืฒืฉืคื™ืœืŸ
- ืึทืจื•ื™ืกืคื™ืจืŸ
โ€”โ€” ื‘ืฒืฉืคื™ืœืŸ
ื“ืึทื˜ืŸ ืคึผืจืึทืกืขืกื™ื ื’
- ื™ืžืคึผืึธืจื˜ ืื•ืŸ ืคึผืจืึทืกืขืกื™ื ื’ ืคื•ืŸ ื“ืึทื˜ืŸ ืคึฟื•ืŸ ื˜ืงืกื˜
- ื™ืžืคึผืึธืจื˜ ืื•ืŸ ืคึผืจืึทืกืขืกื™ื ื’ ืคื•ืŸ ื“ืึทื˜ืŸ ืคึฟื•ืŸ MS Excel
ืึทืจื‘ืขื˜ ืžื™ื˜ ื‘ื™ืœื“ืขืจ
- ื•ื•ืืก ืงืขื ืกื˜ื• ื˜ื•ืŸ?
- ืคึผืจืึทืกืขืกื™ื ื’ ืึท ื–ืึทืžืœื•ื ื’ ืคื•ืŸ ื‘ื™ืœื“ืขืจ
ืึทืจื‘ืขื˜ ืžื™ื˜ ื’ืขื–ื•ื ื˜
- ื‘ื™ื™ึทืฉืคึผื™ืœ
ื™ืžืคึผืึธืจื˜ื™ื ื’ ืื•ืŸ ืคึผืจืึทืกืขืกื™ื ื’ ื“ืึทื˜ืŸ ืคื•ืŸ ื•ื•ืขื‘ ื–ื™ื™ึทื˜ืœืขืš
- ืึทืจื™ื™ึทื ืคื™ืจ ืคื•ืŸ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ืคื•ืŸ โ€‹โ€‹ื“ื™ ื•ื•ืขื‘ื–ื™ื™ื˜ืœ ืคื•ืŸ ื“ื™ ื”ื•ื™ืคื˜ ื‘ืึทื ืง ืคื•ืŸ ื“ื™ ืจื•ืกื™ืฉืข ืคืขื“ืขืจื™ื™ืฉืึทืŸ
- ืœื™ื™ื–ื•ื ื’
โ€”โ€” ืงื™ืฆืขืจ
- ื™ืžืคึผืึธืจื˜ื™ื ื’ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ืคื•ืŸ โ€‹โ€‹ื“ื™ Yandex.Dictionaries ื•ื•ืขื‘ื–ื™ื™ื˜ืœ
ืึทืจื‘ืขื˜ ืžื™ื˜ ื“ื™ API
- VKontakte API
-- ืขืจืฉื˜ืข ื˜ืจื™ื˜
โ€”โ€” AccessToken
โ€”โ€” ืึท ื‘ื™ื™ืฉืคึผื™ืœ ืคื•ืŸ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื“ื™ VKontakte API
- ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ืึทืคึผื™ ืคืึทืกืขื‘ืึธืึธืง, ื˜ื•ื•ื™ื˜ื˜ืขืจ, ื™ื ืกื˜ืึทื’ืจืึทื

2.6 | ืึทืจื‘ืขื˜ ืžื™ื˜ ืึท ื’ืขื‘ื•ื™ื˜-ืื™ืŸ Wolfram ืงื•ืจืึทื˜ืขื“ ื“ืึทื˜ืึทื‘ื™ื™ืกื™ื–, ื™ื ืึทื’ืจื™ื™ืฉืึทืŸ ืžื™ื˜ Wolfram|Alpha


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขืกื™ืกื˜ืขื-ื‘ืจื™ื™ื˜ ืึทืคึผืึทืจืึทื˜ ืฉื˜ื™ืฆืŸ
โ€” ืขืจืฉื˜ืŸ ื‘ืื ื•ืฅ
- ื‘ื™ื™ึทืฉืคึผื™ืœ ืคื•ืŸ ื ื•ืฆืŸ ืื™ืŸ ื—ืฉื‘ื•ื ื•ืช
- ืกืึทืœื•ื•ื™ื ื’ ืกื™ืกื˜ืขืžืขืŸ ืคื•ืŸ ื™ืงื•ื•ื™ื™ื–ืฉืึทื ื– ืžื™ื˜ ืงื•ื•ืึทื ื˜ืึทื˜ื™ื– ืžื™ื˜ ื“ื™ืžืขื ืฉืึทื ื–:
โ€”โ€” ื“ื™ืžืขื ืฉืึทื ืึทืœ ืึทื ืึทืœื™ืกื™ืก (Pi-ื˜ืขืึธืจืขื):
ื ื™ืฆืŸ ื“ืขื ื‘ื™ื™ึทืฉืคึผื™ืœ ืคื•ืŸ ื“ื™ ืคึผืจืึธื‘ืœืขื ืคื•ืŸ ื’ืจืึทื•ื•ื™ื˜ื™ื™ืฉืึทื ืึทืœ ื™ื ืกื˜ืึทื‘ื™ืœื™ื˜ื™ ืคื•ืŸ ืึท ืžื™ื˜ืœ
โ€”โ€”โ€” ื”ืขืœืคืขืจ ืงืื•ื“
--- ืœื™ื™ื–ื•ื ื’
--- ืžืกืงื ื•ืช
ืขืžื‘ืขื“ื™ื“ ื“ืึทื˜ืึทื‘ื™ื™ืกื™ื–
- ืึทืœืข ืคึฟืขื™ึดืงื™ื™ื˜ืŸ ืคึฟืึทืจ ืืจื‘ืขื˜ืŸ ืžื™ื˜ Wolfram Research ืงื•ืจืึทื˜ืขื“ ื“ืึทื˜ืึทื‘ื™ื™ืกื™ื–
โ€” ื‘ื™ื™ืฉืคื™ืœืŸ
โ€”โ€” ืฉืึทืคึฟืŸ ืึท ื•ื•ืขืœื˜ ืžืึทืคึผืข ืงืึธืœื™ืจื˜ ืœื•ื™ื˜ ื“ื™ ื’ื“ืคึผ ืžื“ืจื’ื”
โ€”โ€” ืคึผืขืจื™ืึธื“ื™ืฉ ื˜ื™ืฉ ืคื•ืŸ ื›ืขืžื™ืฉืข ืขืœืขืžืขื ื˜ืŸ ืžื™ื˜ืŸ ื ืืžืขืŸ. ื“ื™ ื™ ืžืขื ื“ืขืœืขืขื•ื•
- ื•ื•ื™ ืึทื–ื•ื™ ื˜ืึธืŸ ืื™ืš ืจืึทื˜ืขื•ื•ืขืŸ Wolfram Research ืงื•ืจืึทื˜ืขื“ ื“ืึทื˜ืึทื‘ื™ื™ืกื™ื– ืคึฟืึทืจ ืจืขื’ืข ืึทืงืกืขืก?
โ€”โ€” ืœืขืึธื ื™ื“ ืฉื™ืคืจื™ื ืก ื‘ืึทืฉืœื•ืก...
--- ืงืื•ื“
โ€”โ€”โ€” ื‘ื™ื™ึทืฉืคึผื™ืœ ืคื•ืŸ ืึทืจื‘ืขื˜
ืฉืคึผืจืึทืš ืขื ื˜ื™ื˜ื™
- (Ctrl + =) - ื‘ืึทืงื•ืžืขืŸ ืึท ืžืึธื“ื•ืœืข ืคึฟืึทืจ ืœืึธื•ืงืึทืœื™ ืงืึทื ื•ื•ืขืจื˜ื™ื ื’ ืึท ืคืจื™ื™-ืคืึธืจืขื ื‘ืขื˜ืŸ ืื™ืŸ ื“ื™ Wolfram ืฉืคึผืจืึทืš ืคึฟืึธืจืžืึทื˜
- ืขื ื˜ื™ื˜ื™
- Entity Value
- EntityClass
- EntityProperties, EntityProperty
โ€” ื“ื™ืคืขืจืขื ืฆื™ืืฆื™ืข ืขื ื˜ื™ื˜ื™ ื“ื•ืจืš ืื•ื™ืกื–ืขืŸ
ืื™ื‘ืขืจื–ืขืฆืขืจ ื™ื‘ืขืจื–ืขืฆืขืจ
- ืจืฉื™ืžื” ืคื•ืŸ ื™ื ื˜ืขืจืคึผืจื™ื˜ื™ื™ืฉืึทืŸ ื˜ื™ื™ืคึผืก
- ืคึฟื•ื ืงืฆื™ืข ื™ื‘ืขืจื–ืขืฆืขืจ
- ืคึฟื•ื ืงืฆื™ืข ืกืขืžืึทื ื˜ื™ืง ื™ื ื˜ืขืจืคึผืจื™ื˜ื™ื™ืฉืึทืŸ
- ืคึฟื•ื ืงืฆื™ืข ืกืขืžืึทื ื˜ื™ืงื™ืžืคึผืึธืจื˜
ื™ื ื˜ืขื’ืจืึทื˜ื™ืึธืŸ ืžื™ื˜ Wolfram|Alpha
- ืคืจื™ื™ ืคืึธืจืขื ืึทืจื™ื™ึทื ืฉืจื™ื™ึทื‘ (= ืื™ืŸ ื“ื™ ืึธื ื”ื™ื™ื‘ ืคื•ืŸ ื“ื™ ืฆืขืœ ืึทืจื™ื™ึทื ืฉืจื™ื™ึทื‘)
โ€”โ€” ื‘ืฒืฉืคื™ืœืŸ
- ืœืืงืืœืข ืคืจื™ื™-ืคืึธืจืขื ืึทืจื™ื™ึทื ืฉืจื™ื™ึทื‘ (Ctrl + = ืขืจื’ืขืฅ ืื™ืŸ ื“ื™ ืึทืจื™ื™ึทื ืฉืจื™ื™ึทื‘ ืฆืขืœ
-- ื‘ื™ื™ึทืฉืคึผื™ืœ
- ื’ืึทื ืฅ ืจืขื–ื•ืœื˜ืึทื˜ ืคื•ืŸ ื“ื™ Wolfram | ืึทืœืคืึท ืึธื ืคึฟืจืขื’ (== ืื™ืŸ ื“ื™ ืึธื ื”ื™ื™ื‘ ืคื•ืŸ ื“ื™ ื™ื ืคึผื•ื˜ ืฆืขืœ)
โ€”โ€” ืขื˜ืœืขื›ืข ื‘ื™ื™ืฉืคื™ืœืŸ ืคื•ืŸ ื ื™ืฆืŸ Wolfram|Alpha
--- ืžืื˜ืขืžืื˜ื™ืง
โ€”โ€”โ€” ืคื™ื–ื™ืง
โ€”โ€”โ€” ื›ืขืžื™ืข
โ€”โ€”โ€” ืžืึทืฉืžืึธืขืก ื˜ืขืึธืจื™ืข, ืกื˜ืึทื˜ื™ืกื˜ื™ืง ืื•ืŸ ื“ืึทื˜ืŸ ืึทื ืึทืœื™ืกื™ืก
โ€”โ€”โ€” ื•ื•ืขื˜ืขืจ ืื•ืŸ ืคืืจื‘ื™ื ื“ืขื ืข ืขื ื™ื ื™ื
โ€”โ€”โ€” ืื™ื ื˜ืขืจื ืขื˜ ืื•ืŸ ืงืืžืคื™ื•ื˜ืขืจ ืกื™ืกื˜ืขืžืขืŸ
--- ืžื•ื–ื™ืง
โ€”โ€”โ€” ืฉืคืฒื–, ื“ืขืจื ืขืจื•ื ื’, ื’ืขื–ื•ื ื˜
- ืคึฟื•ื ืงืฆื™ืข WolframAlpha
โ€”โ€” ื‘ื™ื™ึทืฉืคึผื™ืœ 1: Euler-Venn ื“ื™ื™ืึทื’ืจืึทืžื– ืื•ืŸ ืœืึธื’ื™ืง ืกืขืจืงืึทืฅ ืคึฟืึทืจ ื‘ื•ืœื™ืึทืŸ ืึทืœื’ืขื‘ืจืึท ืคืึทื ื’ืงืฉืึทื ื– ืื™ืŸ ื“ืจื™ื™ ื•ื•ืขืจื™ืึทื‘ืึทืœื–.
โ€”โ€” ื‘ื™ื™ึทืฉืคึผื™ืœ 2: ื’ืขืคึฟื™ื ืขืŸ ื“ื™ ืงืœืึธื•ืกืึทืกื˜ ื’ืขื”ื™ื™ืกืŸ ืคืืจื‘ืŸ ืฆื• ืึท ื’ืขื’ืขื‘ืŸ ืื™ื™ื ืขืจ

3 | ืืจื‘ืขื˜ืŸ ืžื™ื˜ Wolfram Cloud: ืงืจื™ื™ื™ื˜ื™ื ื’ ื“ื™ืจืขืงื˜ ืึทืคึผื™ืก, ืึทืจื™ื™ึทื ืฉืจื™ื™ึทื‘ ืคืืจืžืขืŸ, CloudCDF, ืขื˜ืง.


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขื•ื•ืึธืก ืื™ื– Wolfram Cloud?
โ€” ืคึฟื•ืŸ ืฐืึธืก ื‘ืึทืฉื˜ืฒื˜ Wolfram Cloud?
- ื•ื•ืึธืก ืงืขื ืขืŸ ืื™ืจ ื˜ืึธืŸ ืžื™ื˜ Wolfram Cloud?
ื•ื•ืึธืœืคืจืึทื ืคึผืจืึธื’ืจืึทืžืžื™ื ื’ ืงืœืึธื•ื“
โ€” Wolfram ืคึผืจืึธื’ืจืึทืžืžื™ื ื’ ืงืœืึธื•ื“ ืึทืงืึทื•ื ื˜ ื˜ื™ื™ืคึผืก ื•ื•ืึธืœืคืจืึทื ืคึผืจืึธื’ืจืึทืžืžื™ื ื’ ืงืœืึธื•ื“ ืึทืงืึทื•ื ื˜ ื˜ื™ื™ืคึผืก
โ€” ื•ื•ืึธืœืงืŸ ื”ืœื•ืื•ืช
ื•ื•ืึธืœืงืŸ ืคืึทื ื’ืงืฉืึทื ื– ืื™ืŸ Mathematica ืื•ืŸ Wolfram ื“ืขืกืงื˜ืึธืคึผ
- ืคืึทื ื’ืงืฉืึทื ื– ืคึฟืึทืจ ื“ื™ืจืขืงื˜ ืึทืจื‘ืขื˜ ืžื™ื˜ ื“ื™ ื•ื•ืึธืœืงืŸ, ื•ื•ื™ ื’ืขื–ื•ื ื˜ ื•ื•ื™ ื“ื™ ื•ื•ืึธืก ืงืขื ืขืŸ ืึทืจื‘ืขื˜ืŸ ืžื™ื˜ ื•ื•ืึธืœืงืŸ ืึทื‘ื“ื–ืฉืขืงืฅ.
- ื•ื•ืึธืœืงืŸ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ืคืึทื ื’ืงืฉืึทื ื–
- CloudAccountData - ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ื•ื•ืขื’ืŸ ื“ื™ื™ืŸ ืงืœืึธื•ื“ ื—ืฉื‘ื•ืŸ
- CloudConnect, CloudDisconnect - ืงืึทื ืขืงื˜ื™ื ื’ ืฆื• ืึธื“ืขืจ ื“ื™ืกืงืึทื ืขืงื˜ื™ื ื’ ืคื•ืŸ ื“ื™ ืงืœืึธื•ื“
- CloudObjects - ื“ื™ื™ืŸ ื•ื•ืึธืœืงืŸ ืึทื‘ื“ื–ืฉืขืงืฅ
- $CloudCredits ื‘ื ื™ืžืฆื - ื ื•ืžืขืจ ืคื•ืŸ ื‘ื ื™ืžืฆื ื•ื•ืึธืœืงืŸ ืงืจืขื“ื™ืฅ
ื•ื•ืึธืœืงืŸ ืฆื•ื‘ื™ื ื“, ืขืจืฉื˜ืขืจ ืกื˜ืขืคึผืก
โ€” ื”ื•ื™ืคื˜ึพืคืขื ืฆื˜ืขืจ
- ื“ื™ื™ืŸ ื—ืฉื‘ื•ืŸ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ืคึฟืขื ืฆื˜ืขืจ
- ื ืคึฟืขื ืฆื˜ืขืจ ืžื™ื˜ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ื•ื•ืขื’ืŸ ื“ื™ ื ื•ืฆืŸ ืคื•ืŸ ื“ื™ื™ืŸ ืงืœืึธื•ื“ ืึทื‘ื“ื–ืฉืขืงืฅ ืื•ืŸ ืงืœืึธื•ื“ ืงืจืขื“ื™ืฅ
โ€” ื ื™ื™ืขืจ ื“ืืงื•ืžืขื ื˜ ืคืขื ืฆื˜ืขืจ
ืคื•ื ืงืฆื™ืึธื ื™ืจืŸ FormFunction
- ืฆื™ืœ ืื•ืŸ ืกื™ื ื˜ืึทืงืก
โ€” ื“ืข ืจ ืคืฉื•ื˜ืข ืจ ื‘ืฒืฉืคื™ืœ
- CloudDeploy
- ื˜ื™ื™ืคึผืก ืคื•ืŸ ื•ื•ืขืจื™ืึทื‘ืึทืœื–
- ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื•ื•ืขืจื™ืึทื‘ืึทืœื–
โ€”โ€” โ€žืื™ื‘ืขืจื–ืขืฆืขืจโ€œ ืคืืจืืžืขื˜ืขืจ
โ€”โ€” "ื“ื™ืคืึธืœื˜" ืคึผืึทืจืึทืžืขื˜ืขืจ
โ€”โ€” "ืื™ื ืคึผื•ื˜" ืคึผืึทืจืึทืžืขื˜ืขืจ
โ€”โ€” "ืœืึทื‘ืขืœ" ืคึผืึทืจืึทืžืขื˜ืขืจ
โ€”โ€” โ€œื”ื™ืœืฃโ€ ืคึผืึทืจืึทืžืขื˜ืขืจ
โ€”โ€” "ื”ื™ื ื˜" ืคึผืึทืจืึทืžืขื˜ืขืจ
- ืงืึทืกื˜ืึทืžื™ื™ื– ื“ื™ ืื•ื™ืกื–ืขืŸ ืคื•ืŸ ื“ื™ ืคืึธืจืขื
- ืึทืคึผืคึผืขืึทืจืึทื ืกืข ืจื•ืœืขืก
โ€”โ€”ืคืืจืื˜ืขืžืข
- ืžืขื’ืœืขืš ืจืขื–ื•ืœื˜ืึทื˜ ืคึฟืึธืจืžืึทื˜ื™ืจื•ื ื’ืขืŸ
โ€” ืึทืจื™ื™ื ืœื™ื™ื’ืŸ ืจื•ืกื™ืฉืขืจ ื˜ืขืงืกื˜
-- ื‘ื™ื™ึทืฉืคึผื™ืœ
โ€” ื‘ื™ื™ืฉืคื™ืœืŸ
โ€”โ€” ืฉืึทืคึฟืŸ ืึท ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ ืฆื• ืกืึธืœื•ื•ืข ื“ื™ ื™ืงื•ื•ื™ื™ื–ืฉืึทืŸ
โ€”โ€” ืฉืึทืคึฟืŸ ืึท ื‘ื™ืœื“ ืคึผืจืึทืกืขืกื™ื ื’ ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ
โ€”โ€” ืฉืึทืคึฟืŸ ืึท ื“ื–ืฉื™ืึทื’ืจืึทืคื™ืง ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ ืžื™ื˜ ืงืœื•ื’ ืคืขืœื“ืขืจ
ืคื•ื ืงืฆื™ืึธื ื™ืจืŸ APIFunction
โ€” ื‘ื™ื™ืฉืคื™ืœืŸ
โ€”โ€” ืฉืึทืคึฟืŸ ืึท ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ ืฆื• ืกืึธืœื•ื•ืข ื“ื™ ื™ืงื•ื•ื™ื™ื–ืฉืึทืŸ
โ€”โ€” ืฉืึทืคึฟืŸ ืึท ื“ื–ืฉื™ืึทื’ืจืึทืคื™ืง ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ ืžื™ื˜ ืงืœื•ื’ ืคืขืœื“ืขืจ

4 | CDF ื˜ืขื›ื ืึธืœืึธื’ื™ืข - ืจืขื’ืข ืขืžื‘ืขื“ื“ื™ื ื’ ืคื•ืŸ ื™ื ื˜ืขืจืึทืงื˜ื™ื•ื• ืึทื‘ื“ื–ืฉืขืงืฅ ื‘ืืฉืืคืŸ ืื™ืŸ Mathematica ืื™ืŸ ื•ื•ืขื‘ ื–ื™ื™ึทื˜ืœืขืš, ืกืึทื˜ืึทืœื˜ื™ื–. ื ื™ืฆืŸ ืคืึทืจื˜ื™ืง ื™ื ื˜ืขืจืึทืงื˜ื™ื•ื• ืึทื‘ื“ื–ืฉืขืงืฅ ืคื•ืŸ ื“ื™ Wolfram ื“ืขืžืึทื ืกื˜ืจื™ื™ืฉืึทื ื– ืคึผืจืึธื™ืขืงื˜ ื•ื•ืขื‘ื–ื™ื™ื˜ืœ ืื™ืŸ ื“ื™ื™ืŸ ืคึผืจืึทื“ื–ืฉืขืงืก ืื•ืŸ ืžืึธื“ื™ืคื™ืฆื™ืจืŸ ื–ื™ื™. ืคืึทืงื˜ื™ืฉ-ืœืขื‘ืŸ ื‘ื™ื™ืฉืคื™ืœืŸ ืื•ืŸ ื’ืขืฉืขืคื˜ ืึทืคึผืœืึทืงื™ื™ืฉืึทื ื–


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขCDF - ืงืึธืžืคึผื•ื˜ืึทื‘ืœืข ื“ืึธืงื•ืžืขื ื˜ ืคึฟืึธืจืžืึทื˜ - ืงืึธืžืคึผื•ื˜ืึทื‘ืœืข ื“ืึธืงื•ืžืขื ื˜ ืคึฟืึธืจืžืึทื˜
- CDF ื˜ืขื›ื ืึธืœืึธื’ื™ืข
- ืงื•ืจืฅ ืคืึทืจื’ืœื™ื™ึทืš ืžื™ื˜ ืื ื“ืขืจืข ืคึฟืึธืจืžืึทื˜ื™ืจื•ื ื’ืขืŸ
โ€” ืกื˜ืึทื’ืขืก ืคื•ืŸ ืฉืึทืคึฟืŸ ืึท CDF
โ€”โ€” ืื™ืœื•ืกื˜ืจื™ืจื˜ืข ื˜ืจื™ื˜
โ€” ืคืึทืงื˜ื™ืฉ ื‘ื™ื™ืฉืคื™ืœืŸ
- ื•ื•ืึธืœืคืจืึทื ื“ืขืžืึทื ืกื˜ืจื™ื™ืฉืึทื ื– ืคึผืจืึธื™ืขืงื˜
ืงืจื™ื™ื™ื˜ื™ื ื’ ืึท CDF ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ ืžืึทื ื™ืคึผื•ืœืึทื˜ืข
โ€” ืฉืจื™ื˜ 1. ืงืจื™ื™ื™ื˜ื™ื ื’ ืึท ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ
โ€” ืฉืจื™ื˜ 2. ื”ื™ื˜ ืขืก ืื™ืŸ CDF ืคึฟืึธืจืžืึทื˜
โ€” ืฉืจื™ื˜ 3. ื™ื ืกืขืจื˜ื™ื ื’ ืื™ืŸ ืึท ื•ื•ืขื‘ ื‘ืœืึทื˜
ืงืจื™ื™ื™ื˜ื™ื ื’ CDF ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ DynamicModule
โ€” ืฉืจื™ื˜ 1. ืงืจื™ื™ื™ื˜ื™ื ื’ ืึท ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ
โ€” ืฉืจื™ื˜ 2. ื”ื™ื˜ ืขืก ืฆื• CDF
โ€” ืฉืจื™ื˜ 3. ื™ื ืกืขืจื˜ื™ื ื’ ืื™ืŸ ืึท ื•ื•ืขื‘ ื‘ืœืึทื˜
โ€” ื ืืš ื ื‘ื™ื™ืฉืคื™ืœ ืคื•ืŸ ื ืงืืžืคืœื™ืฆื™ืจื˜ืขืจ ืงื“ืฃ
ืฉืืคืŸ ืคืึทืจื˜ื™ืง ื•ื•ืขื‘ ื–ื™ื™ึทื˜ืœืขืš ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ CDF
- ื‘ื™ื™ึทืฉืคึผื™ืœ
EnterpriseCDF
- ื“ื™ืคืขืจืึทื ืกื™ื– ืฆื•ื•ื™ืฉืŸ CDF ืื•ืŸ EnterpriseCDF
- ื™ืงืขืจื“ื™ืง ืคืึทืจื’ืœื™ื™ึทืš ืคื•ืŸ CDF ืื•ืŸ EnterpriseCDF
- ื“ื™ื˜ื™ื™ืœื“ ืคืึทืจื’ืœื™ื™ึทืš ืคื•ืŸ CDF, EnterpriseCDF, Wolfram Player Pro ืื•ืŸ Mathematica
CloudCDF
- ื•ื•ืึธืก ืื™ื– CloudCDF?
- ื‘ื™ื™ึทืฉืคึผื™ืœ ืคื•ืŸ ืงืจื™ื™ื™ื˜ื™ื ื’ CloudCDF
โ€” โ€” ื‘ืฒืฉืคื™ืขืœ 1
โ€” โ€” ื‘ืฒืฉืคื™ืขืœ 2

5 | ืึทืจื‘ืขื˜ ืžื™ื˜ Wolfram Language ืื•ืŸ Mathematica, ืคืึทืจ-ืื™ื ืกื˜ืึทืœื™ืจืŸ ืื•ืŸ ืคืจื™ื™ ืื•ื™ืฃ Raspberry Pi (ืžื™ื˜ Raspbian ืึทืคึผืขืจื™ื™ื˜ื™ื ื’ ืกื™ืกื˜ืขื)


ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืœืขืงืฆื™ืขRaspberry Pi, ืขืจืฉื˜ืขืจ ื‘ืึทืงืึทื ื˜ืขืจ
- ื•ื•ืืก ืื™ื– ื“ืืก?
โ€” ืฐืื• ืงืืŸ ืื™ืš ืขืก ืงื•ื™ืคืŸ?
- ื•ื•ื• ืื•ืŸ ื•ื•ื™ ืฆื• ื™ื ืกื˜ืึทืœื™ืจืŸ ื“ื™ ืึทืก, ืžื™ื˜ Wolfram ืฉืคึผืจืึทืš ืฉื˜ื™ืฆืŸ
Raspberry Pi ืื•ืŸ Wolfram ืฉืคึผืจืึทืš
โ€” ืคึผืจืึธื™ืขืงื˜ ื‘ืœืึทื˜
โ€” ื“ืืงื•ืžืขื ื˜ืืฆื™ืข ื‘ืœืื˜
- ื•ื•ื™ Raspberry Pi ืงื•ืงื˜ ื•ื•ื™ ื ืึธืš ื™ื ืกื˜ืึทืœื™ืจื•ื ื’
- ื“ืขืจ ื’ืขื“ืึทื ืง ืคื•ืŸ ืคึผืจืึธื’ืจืึทืžืžื™ื ื’ ืื™ืŸ Wolfram ืฉืคึผืจืึทืš ืื•ื™ืฃ Raspberry Pi
Raspberry Pi ืคืึธืจืฉื˜ืขืœื•ื ื’
โ€” ืงืึทืœืงื•ืœื™ืจืŸ ืขื˜ืœืขื›ืข ืงืึธื“
- ืกื˜ืึทื ื“ืึทืจื“ ื’ืขื‘ื•ื™ื˜-ืื™ืŸ Wolfram ื‘ืขื ื˜ืฉืžืึทืจืง
- ืคืึทืจื’ืœื™ื™ึทืš ืžื™ื˜ ืคึผื™ื˜ื”ืึธืŸ ืคืึธืจืฉื˜ืขืœื•ื ื’ ืื•ื™ืฃ Raspberry Pi
ื ื‘ื™ื™ืฉืคึผื™ืœ ืคื•ืŸ ืึท ืคึผืึธืกื˜ ืจืึธื‘ืึธื˜ ื•ื•ืึธืก ืœื•ื™ืคื˜ ืื•ื™ืฃ Raspberry Pi
ื‘ื™ื™ืฉืคื™ืœืŸ ืคื•ืŸ ืืจื‘ืขื˜ืŸ ืžื™ื˜ Raspberry Pi
- ืฉืึทืคื•ื ื’ ืคื•ืŸ ืึท ื’ืคึผืก ื˜ืจืึทืงืขืจ
โ€”โ€” ืื™ื”ืจ ืฐืขื˜ ื“ืืจืคืขืŸ
โ€”โ€” ืงื•ืง ื ืืš ืืกื™ืคื”
โ€”โ€” ืคึผืจืึธื’ืจืึทื ืคึฟืึทืจ ืžืื˜ืขืžืื˜ื™ืง ืื•ื™ืฃ Raspberry Pi
โ€” ื ืขืžืขืŸ ื ืคืึธื˜ืึธ
โ€”โ€” ืื™ื”ืจ ืฐืขื˜ ื“ืืจืคืขืŸ
โ€”โ€” ืงื•ืง ื ืืš ืืกื™ืคื”
โ€”โ€” ืคึผืจืึธื’ืจืึทื ืคึฟืึทืจ ืžืื˜ืขืžืื˜ื™ืง ืื•ื™ืฃ Raspberry Pi
- ื ื™ืฆืŸ GPIO
โ€”โ€” ืื™ื”ืจ ืฐืขื˜ ื“ืืจืคืขืŸ
โ€”โ€” ืงื•ืง ื ืืš ืืกื™ืคื”
โ€”โ€” ืคึผืจืึธื’ืจืึทื ืคึฟืึทืจ ืžืื˜ืขืžืื˜ื™ืง ืื•ื™ืฃ Raspberry Pi
โ€” ืื ื“ืขืจืข ื‘ื™ื™ืฉืคื™ืœืŸ
ื•ื•ื• ืงืขืŸ ืื™ืš ื’ืขืคึฟื™ื ืขืŸ ืžืขืจ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ื•ื•ืขื’ืŸ Wolfram ืฉืคึผืจืึทืš ืื•ืŸ Raspberry Pi ื™ื ืึทื’ืจื™ื™ืฉืึทืŸ?

ืื™ืš ืึทื ื˜ืฉื•ืœื“ื™ืงืŸ ืคึฟืึทืจ ื“ื™ ื’ืขื–ื•ื ื˜ ืงื•ื•ืึทืœื™ื˜ืขื˜, ืื™ืŸ ืขื˜ืœืขื›ืข ื•ื•ื™ื“ื™ืืก ืขืก ืื™ื– ื ื™ืฉื˜ ืึทื–ื•ื™ ื’ื•ื˜ ื•ื•ื™ ืื™ืš ื•ื•ืึธืœื˜ ื•ื•ื™.

ืื™ืŸ ื ื™ื™ึทืข ื•ื•ื™ื“ื™ืืก ืื•ืŸ ื•ื•ืขื‘ื™ื ืึทืจืก, ืึทืœืฅ ืื™ื– ื’ื•ื˜ ืžื™ื˜ ื’ืขื–ื•ื ื˜ ืื•ืŸ ื•ื•ื™ื“ืขื ืื™ืŸ 2K. ืคืึทืจื‘ื™ื ื“ืŸ ืื•ื ื“ื–: ื™ืขื“ืขืจ ื•ื•ืึธืš ืขืก ื–ืขื ืขืŸ ืœื™ื™ื•ื• ื‘ืจืึธื“ืงืึทืกืฅ ืื•ื™ืฃ ื“ืขื ืงืึทื ืึทืœ.

ื•ื•ืขื‘ื™ื ืึทืจ ื‘ื™ื™ึทืฉืคึผื™ืœ



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