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How do you simplify the following expression in Sage?

asked 2024-12-27 22:02:47 +0100

mathew1794
13 ●2

updated 2024-12-28 11:27:02 +0100

tmonteil
27443 ●31 ●204 ●518 http://wiki.sagemath.o...

By differentiating a function at 0, I got the following equation in Sage.

(b - f(0))*(c - f(0))*D[0](f)(0) - 1 == 0

How do I make Sage

Plug in f(0) = b+c

Simplify and solve for D[0](f)(0)?

I tried

equation = (b - f(0))*(c - f(0))*D[0](f)(0) - 1 == 0
new_equation = equation.subs({f(0): b+c})
solve(new_equation, D[0](f)(0))

I get the following error

Substitution using function-call syntax and unnamed arguments has been removed. You can use named arguments instead, like EXPR(x=..., y=...)

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Comments

You should tell us how you defined f, so that we can replicate the behaviour you obtain.

tmonteil ( 2024-12-28 11:28:54 +0100 )edit

Note: also asked as Stack Overflow question 79309746.

slelievre ( 2024-12-29 00:13:47 +0100 )edit

f is defined as

a=SR.var('a')
f=function('f')(a)

mathew1794 ( 2024-12-31 23:58:00 +0100 )edit

1 Answer

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answered 2024-12-29 00:12:44 +0100

slelievre
17739 ●22 ●160 ●351 http://carva.org/samue...

The problem could be with how f was defined.

In particular if it was defined as an expression rather than a function.

Be it with SageMath 10.2 or SageMath 10.4, the following input

sage: b, c = SR.var('b, c')
sage: f = function('f')
sage: equation = (b - f(0))*(c - f(0))*D[0](f)(0) - 1 == 0
sage: new_equation = equation.subs({f(0): b + c})
sage: solve(new_equation, D[0](f)(0))

gives the following output

[D[0](f)(0) == 1/(b*c)]

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Last updated: Dec 29 '24

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