SamplePublisher`GrassmannCalculus`
IntegralOptionsRules  |
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
The following is integral 3.121 from Gradshteyn & Ryzhik. It gives a that depends on the value of the parameters.
ConditionalExpression
In[2]:=
Inactive[Integrate],{x,0,1}Activate[%]step1=FullSimplify%,qp∈Reals&&≤0
1
q-px
1
x(1-x)
q
p
Out[2]=
1
∫
0
1
(1-x)x
(q-px)Out[2]=
ConditionalExpression,Re≥1||Re≤0||∉Reals
π
-
qp
q
1-
q
p
q
p
q
p
q
p
Out[2]=
π
1-
qp
q
We can add assumption to the initial Integrate statement but that destroys the nice formatting. Instead we can add the assumptions just before evaluation.
In[3]:=
Inactive[Integrate],{x,0,1}%/.
[Assumptions0<p<q];Activate[%]
1
q-px
1
x(1-x)
 | IntegralOptionsRules |
Out[3]=
1
∫
0
1
(1-x)x
(q-px)Out[3]=
π
q(-p+q)
FormIntegrals
InactiveIntegralTrue
EvaluateFormIntegrals
Integrate
Inactive
In[4]:=
SetEuclideanNSpace[1,{x},"Form"]
0≤x≤1,dx
[%,InactiveIntegralTrue]%/.
[Assumptions0<p<q];Activate[%]
 | FormIntegral |
1
q-px
1
x(1-x)
| EvaluateFormIntegrals |
| IntegralOptionsRules |
Out[4]=
∫
ℴ
dx
(1-x)x
(q-px)Out[4]=
∞
∫
-∞
Boole[0≤x≤1]
(1-x)x
(q-px)Out[4]=
π
q(-p+q)
It is also possible to enter the Assumptions, or other options, directly into the command.
EvaluateFormIntegrals
In[5]:=
SetEuclideanNSpace[1,{x},"Form"]
0≤x≤1,dx
[%,Assumptions0<p<q]
| FormIntegral |
1
q-px
1
x(1-x)
| EvaluateFormIntegrals |
Out[5]=
∫
ℴ
dx
(1-x)x
(q-px)Out[5]=
π
q(-p+q)
 |
|
 |
|
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