Evaluating a derivative in gp/pari
Specifically, I'm trying to evaluate the derivative of the Weierstrass P function at a specific point.
I know that I can set up a function like the following
p(z) = ellwp([1,I],z);
Which will allow me to input p(z), where z is a copmlex number, and have the output be the desired evaluation of the Weierstrass P function at z.
The problem is, I can't seem to do anything similar with the derivative. For example something like
p(z) = deriv(ellwp([1,I],z));
will return $0$ for any input $z$ (because pari is computing the value of the Weierstrass P function at z and then differentiating the resulting constant).
If there is any way this can be done, I would be grateful to hear about it.
power-series math-software elliptic-functions
asked Dec 3 '18 at 14:42
JonHalesJonHales
381211
add a comment |
Specifically, I'm trying to evaluate the derivative of the Weierstrass P function at a specific point.
I know that I can set up a function like the following
p(z) = ellwp([1,I],z);
Which will allow me to input p(z), where z is a copmlex number, and have the output be the desired evaluation of the Weierstrass P function at z.
The problem is, I can't seem to do anything similar with the derivative. For example something like
p(z) = deriv(ellwp([1,I],z));
will return $0$ for any input $z$ (because pari is computing the value of the Weierstrass P function at z and then differentiating the resulting constant).
If there is any way this can be done, I would be grateful to hear about it.
power-series math-software elliptic-functions
asked Dec 3 '18 at 14:42
JonHalesJonHales
381211
add a comment |
Specifically, I'm trying to evaluate the derivative of the Weierstrass P function at a specific point.
I know that I can set up a function like the following
p(z) = ellwp([1,I],z);
Which will allow me to input p(z), where z is a copmlex number, and have the output be the desired evaluation of the Weierstrass P function at z.
The problem is, I can't seem to do anything similar with the derivative. For example something like
p(z) = deriv(ellwp([1,I],z));
will return $0$ for any input $z$ (because pari is computing the value of the Weierstrass P function at z and then differentiating the resulting constant).
If there is any way this can be done, I would be grateful to hear about it.
power-series math-software elliptic-functions
asked Dec 3 '18 at 14:42
JonHalesJonHales
381211
Specifically, I'm trying to evaluate the derivative of the Weierstrass P function at a specific point.
I know that I can set up a function like the following
p(z) = ellwp([1,I],z);
Which will allow me to input p(z), where z is a copmlex number, and have the output be the desired evaluation of the Weierstrass P function at z.
The problem is, I can't seem to do anything similar with the derivative. For example something like
p(z) = deriv(ellwp([1,I],z));
will return $0$ for any input $z$ (because pari is computing the value of the Weierstrass P function at z and then differentiating the resulting constant).
If there is any way this can be done, I would be grateful to hear about it.
power-series math-software elliptic-functions
power-series math-software elliptic-functions
asked Dec 3 '18 at 14:42
JonHalesJonHales
381211
asked Dec 3 '18 at 14:42
JonHalesJonHales
381211
asked Dec 3 '18 at 14:42
JonHalesJonHales
381211
asked Dec 3 '18 at 14:42
JonHalesJonHales
381211
asked Dec 3 '18 at 14:42
JonHalesJonHales
381211
381211
add a comment |
add a comment |
1 Answer
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Look at the help:
? ?ellwp
ellwp(w,{z='x},{flag=0}): computes the value at z of the Weierstrass P function
attached to the lattice w, as given by ellperiods. Optional flag means 0
(default), compute only P(z), 1 compute [P(z),P'(z)].
So you can compute the function value and the derivative in one call
? ellwp([1,I], 1.2 + 2.1*I, 1)
%1 = [12.28012262 - 15.62055727*I, -28.28677598 + 177.9634914*I]
Now define the derivative dp(z) and get
? dp(z) = my{local a; a=ellwp([1,I],z,1); a[2]}
%2 = (z)->mylocala;a=ellwp([1,I],z,1);a[2]
? dp(1.2+2.1*I)
%3 = -28.28677598 + 177.9634914*I
answered Dec 3 '18 at 16:00
gammatestergammatester
16.7k21632
I knew it must be something simple, thank you very much.
– JonHales
Dec 3 '18 at 16:27
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
Look at the help:
? ?ellwp
ellwp(w,{z='x},{flag=0}): computes the value at z of the Weierstrass P function
attached to the lattice w, as given by ellperiods. Optional flag means 0
(default), compute only P(z), 1 compute [P(z),P'(z)].
So you can compute the function value and the derivative in one call
? ellwp([1,I], 1.2 + 2.1*I, 1)
%1 = [12.28012262 - 15.62055727*I, -28.28677598 + 177.9634914*I]
Now define the derivative dp(z) and get
? dp(z) = my{local a; a=ellwp([1,I],z,1); a[2]}
%2 = (z)->mylocala;a=ellwp([1,I],z,1);a[2]
? dp(1.2+2.1*I)
%3 = -28.28677598 + 177.9634914*I
answered Dec 3 '18 at 16:00
gammatestergammatester
16.7k21632
I knew it must be something simple, thank you very much.
– JonHales
Dec 3 '18 at 16:27
add a comment |
Look at the help:
? ?ellwp
ellwp(w,{z='x},{flag=0}): computes the value at z of the Weierstrass P function
attached to the lattice w, as given by ellperiods. Optional flag means 0
(default), compute only P(z), 1 compute [P(z),P'(z)].
So you can compute the function value and the derivative in one call
? ellwp([1,I], 1.2 + 2.1*I, 1)
%1 = [12.28012262 - 15.62055727*I, -28.28677598 + 177.9634914*I]
Now define the derivative dp(z) and get
? dp(z) = my{local a; a=ellwp([1,I],z,1); a[2]}
%2 = (z)->mylocala;a=ellwp([1,I],z,1);a[2]
? dp(1.2+2.1*I)
%3 = -28.28677598 + 177.9634914*I
answered Dec 3 '18 at 16:00
gammatestergammatester
16.7k21632
I knew it must be something simple, thank you very much.
– JonHales
Dec 3 '18 at 16:27
add a comment |
Look at the help:
? ?ellwp
ellwp(w,{z='x},{flag=0}): computes the value at z of the Weierstrass P function
attached to the lattice w, as given by ellperiods. Optional flag means 0
(default), compute only P(z), 1 compute [P(z),P'(z)].
So you can compute the function value and the derivative in one call
? ellwp([1,I], 1.2 + 2.1*I, 1)
%1 = [12.28012262 - 15.62055727*I, -28.28677598 + 177.9634914*I]
Now define the derivative dp(z) and get
? dp(z) = my{local a; a=ellwp([1,I],z,1); a[2]}
%2 = (z)->mylocala;a=ellwp([1,I],z,1);a[2]
? dp(1.2+2.1*I)
%3 = -28.28677598 + 177.9634914*I
answered Dec 3 '18 at 16:00
gammatestergammatester
16.7k21632
Look at the help:
? ?ellwp
ellwp(w,{z='x},{flag=0}): computes the value at z of the Weierstrass P function
attached to the lattice w, as given by ellperiods. Optional flag means 0
(default), compute only P(z), 1 compute [P(z),P'(z)].
So you can compute the function value and the derivative in one call
? ellwp([1,I], 1.2 + 2.1*I, 1)
%1 = [12.28012262 - 15.62055727*I, -28.28677598 + 177.9634914*I]
Now define the derivative dp(z) and get
? dp(z) = my{local a; a=ellwp([1,I],z,1); a[2]}
%2 = (z)->mylocala;a=ellwp([1,I],z,1);a[2]
? dp(1.2+2.1*I)
%3 = -28.28677598 + 177.9634914*I
answered Dec 3 '18 at 16:00
gammatestergammatester
16.7k21632
answered Dec 3 '18 at 16:00
gammatestergammatester
16.7k21632
answered Dec 3 '18 at 16:00
gammatestergammatester
16.7k21632
answered Dec 3 '18 at 16:00
gammatestergammatester
16.7k21632
16.7k21632
I knew it must be something simple, thank you very much.
– JonHales
Dec 3 '18 at 16:27
add a comment |
I knew it must be something simple, thank you very much.
– JonHales
Dec 3 '18 at 16:27
I knew it must be something simple, thank you very much.
– JonHales
Dec 3 '18 at 16:27
I knew it must be something simple, thank you very much.
– JonHales
Dec 3 '18 at 16:27
add a comment |
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