SamplePublisher`GrassmannCalculus`
IntegralSumRules  |
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Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Various forms of Integrate expressions can be broken out.
In[2]:=
Inactive[Integrate][f[x]+g[x],x]%/.
 | IntegralSumRules |
Out[2]=
∫(f[x]+g[x])x
Out[2]=
∫f[x]x+∫g[x]x
In[3]:=
Inactive[Integrate][f[x]+g[x],{x,a,b}]%/.
| IntegralSumRules |
Out[3]=
b
∫
a
Out[3]=
b
∫
a
b
∫
a
In[4]:=
Inactive[Integrate][f[x,y]+g[x,y],x,y]%/.
| IntegralSumRules |
Out[4]=
∫∫(f[x,y]+g[x,y])yx
Out[4]=
∫∫f[x,y]yx+∫∫g[x,y]yx
In[5]:=
Inactive[Integrate][f[x]+g[x],{x,a,b},{y,c,d}]%/.
| IntegralSumRules |
Out[5]=
b
∫
a
d
∫
c
Out[5]=
b
∫
a
d
∫
c
b
∫
a
d
∫
c
FormIntegrals are also broken out.
In[6]:=
SetEuclideanNSpace[1,{x},"Form"]
[Undefined,(f[x]+g[x])dx]%/.
| FormIntegral |
| IntegralSumRules |
Out[6]=
∫
ℴ
Out[6]=
∫
ℴ
∫
ℴ
In[7]:=
SetEuclideanNSpace[2,{x,y},"Form"]
[Ball[{0,0},2],(f[x,y]+g[x,y])dx⋀dy]%/.
| FormIntegral |
| IntegralSumRules |
Out[7]=
∫
ℴ
Out[7]=
∫
ℴ
∫
ℴ
In[8]:=
SetEuclideanNSpace[2,{x,y},"Form"]
[Ball[{0,0},2],(Sin[x+y]+Cos[x-y])dx⋀dy]%/.
%//
%//N
| FormIntegral |
| IntegralSumRules |
| EvaluateFormIntegrals |
Out[8]=
∫
ℴ
Out[8]=
∫
ℴ
∫
ℴ
Out[8]=
4πHypergeometric0F1Regularized[2,-2]
Out[8]=
3.55603
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