Εσωτερική αναπαράσταση παραστάσεων στην Mathematica

Clear["`*"];

FullForm[Hold[a=10]]

a*a/2-x*x+10x+3-D[3x^3-4x^2-x+21,x]+Integrate[6x^2-4,x]/. {a->4,x->2}

FullForm[Hold[a*a/2-x*x+10x+3-D[3x^3-4x^2-x+21,x]+Integrate[6x^2-4,x]/. {a->4,x->2} ]]

ReplaceAll[Plus[Times[a,Times[a,Power[2,-1]]],Times[-1,Times[x,x]],Times[10,x],3,Times[-1,D[Plus[Times[3,Power[x,3]],Times[-1,Times[4,Power[x,2]]],Times[-1,x],21],x]],Integrate[Plus[Times[6,Power[x,2]],-4],x]],List[Rule[a,4],Rule[x,2]]]

Head[10]

Head[x]

Head[1.2]

Head["abc"]

E^(2.0Pi I)

Head[%]

Head[2+3 I]

Head[2/5]

{Head[Pi], Head[N[Pi]]}

{FullForm[{1,2,3}], Head[{1,2,3}]}

{FullForm[a+b], Head[a+b]}

{FullForm[a*b+c], Head[a*b+c]}

{FullForm[Integrate[3x^2,{x,1,2}]],FullForm[Hold[Integrate[3x^2,{x,1,2}]]]}

{D[x^n,x], FullForm[D[x^n,x]], FullForm[Hold[D[x^n,x]]]}

FullForm[Hold[t = z + 1;p=a x^2+b x+c]]

{FullForm[w=1],FullForm[w:=1], FullForm[Hold[w=1]], FullForm[Hold[w:=1]]}

{Head[Sin[x]], Head[Cos[x]], Head[Log[x]],Head[Abs[x]],Head[Exp[x]]}

{Sin[3Pi/2],Head[Sin[3Pi/2]],FullForm[Hold[Head[Sin[3Pi/2]]]]}

{Head[Sqrt[x]], FullForm[Sqrt[x]]}

{Head[x/(2y)], FullForm[x/(2y)]}

{Head[3+4I], Head[a+b I], FullForm[3+4I], FullForm[a+b I]}

{Head[x->y], FullForm[x->y]}

Τύπος παράστασης

Head[5]

Head[7/3]

Head[0.78]

Head[x]

Head[3+5]

Head[x+2]

FullForm[x+2]

Head[2+Sin[x]]

Head[Sin[x+7]]

Head[3 * (Tan[2] + 2)]

FullForm[3 * (Tan[2] + 2)]

FullForm[3 * x^(2/3) + 7]

Επιπλέον τελεστές

x=25

x++

x

x+=2

x

x--

--x

x

x==26

x==40

x==a

x===a

x==26==52/2

x!=26

x!=26  || x!=8

(2>1)&&(3>4)

(2>1)&&!(3>4)

Pi<22/7

3 > 2 + 2

5 > 4 && 1 > 2

5>4&&1>2

3>2+2

Αριθμητικά αποτελέσματα - η συνάρτηση Ν

2^100/6

2^100/6.

2^100/(6 Pi)

2^100/(6. Pi)

N[2^100/(6. Pi)]

N[2^100/(6 Pi),50]

N[N[2^100/(6 Pi),16],50]

N[Pi,10]

N[22/7]

N[355/113,10]

Pi<355/113<22/7

Βασικές συναρτήσεις

"Sqrt[]","Exp[ ]",, "Log[ ]" , "Log[b, x]", "Sin[ ]", "Cos[ ]", "Tan[ ]", "ArcSin[ ]","ArcCos[ ]", and "ArcTan[ ]" και άλλες........

Exp[-2] Sin[3 Pi/4]

N[Exp[-2] Sin[3 Pi/4]]

Log[E^5]

Log[2,2^6]

x=.

Integrate[Sin[Abs[-6]x]Cos[Sign[-2]x],x]

Trace[Integrate[Sin[Abs[-6]x]Cos[Sign[-2]x],x]]

Trace[Integrate[Sin[Abs[-6]x]Cos[Sign[-2]x],{x,-Pi,2Pi}]]

f[x_]:=x^2-2

f[x]

f[3]

expr=(x-10)^5

e1[x_]=Expand[x]
e2[x_]:=Expand[x]

e1[expr]

e2[expr]

c[n_,k_]:=n!/(k! (n-k)!)

c[52,5]

Binomial[52,5]

Γραφήματα

Plot[x^2,{x,0,1}]

Plot[{x^2,x},{x,0,3}]

Exp[-Sqrt[x]] Sin[2^x]

Plot[Exp[-Sqrt[x]] Sin[2^x], {x,0,2Pi}, PlotRange->All]

Plot[(E^(-(Sqrt[x]))) Sin[(2^x)],{x,0,2 π},PlotRange->All,MaxRecursion->15]

Plot[Exp[-Sqrt[x]] Sin[2^x], {x,0,2Pi}]

Plot[Exp[-Sqrt[x]] Sin[2^x], {x,0,2Pi}, PlotRange->All]

Plot[(E^(-(Sqrt[x]))) Sin[(2^x)],{x,0,2 π},PlotRange->All,MaxRecursion->15]

Options[Plot]

?PlotDivision

?PlotRange

Plot[{x^E, E^x}, {x,0,4}]

Plot[{x^E, E^x}, {x,0,4},
  PlotStyle->{{Dashing[{.03}]}, {}}]

Plot[{x^E,E^x},{x,0,4},
  PlotStyle->{{Red, Dashing[{.02}]}, {Blue}},
  Frame->True
]

(*   Needs["Graphics`Colors`"];   έκδοση 5.2  *)

AllColors=ColorData["Legacy","Names"];

AllColors