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Coefficient of Polynomial of Differential Forms and displaying List for differential forms

asked 2020-06-21 18:32:55 -0500

whatupmatt gravatar image

The coefficient function gives us the coefficient of a polynomial. For example,

g(x)=3*x^(2)

g.coefficient(x^(2))

Just started learning differential forms, so using notation here- https://ask.sagemath.org/question/403...

U = Manifold(4, 'U')

X. < x,y,z,w > = U.chart()

f = U.diff_form(4, 'f')

f[0,1,2,3]=3*x^(2)

f.display()

(f[0,1,2,3]).coefficient(x^(2))

I want to work backwards. For example, given a 4-form named Form, Form[0,1,2,3] gives me the polynomial of the form. I wish to find the coefficient of this polynomial the same way. So from above, I should be getting 3. But I get:

'ChartFunctionRing_with_category.element_class' object has no attribute 'coefficient'.

Question 1: How do I fix this?

Question 2: Suppose I have a list of 4-forms called List. From the link above, I can view every form in List by doing List[1].display().

However, how do I quickly view all the forms?

List.display() gives me an error so can I only view the forms term by term?

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answered 2020-06-22 06:55:55 -0500

rburing gravatar image

1)

sage: f[0,1,2,3].expr().coefficient(x^2)
3

2)

sage: List = [f]*3
sage: show(LatexExpr('[' + ','.join(latex(f.display()) for f in List) + ']'))

$$[f = 3 \, x^{2} \mathrm{d} x\wedge \mathrm{d} y\wedge \mathrm{d} z\wedge \mathrm{d} w,f = 3 \, x^{2} \mathrm{d} x\wedge \mathrm{d} y\wedge \mathrm{d} z\wedge \mathrm{d} w,f = 3 \, x^{2} \mathrm{d} x\wedge \mathrm{d} y\wedge \mathrm{d} z\wedge \mathrm{d} w]$$

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Great, thanks for your help.

whatupmatt gravatar imagewhatupmatt ( 2020-06-22 08:14:37 -0500 )edit

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Asked: 2020-06-21 18:32:55 -0500

Seen: 48 times

Last updated: Jun 22