How to declare derivatives of a multivariable function as real in order to get Re and Im part of the expression?
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Re and Im work properly, with appropriate assumptions, in the example like this
Assuming[g[_, _] ∈ Reals, Simplify[Im[3*I*g[r, r2] + 45]]]
On the other hand, if the derivative of the function is also present, similar approach does not work
Assuming[(r | g[_, _] | D[g[_, _], _]) ∈ Reals, Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
i.e. does not give back 3*D[g[r, r2], r]
More dramatically,
Assuming[(r | g[_, _] | f[_]) ∈ Reals, Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
gives 3 Re[g[r,r2] (f^′)[r]+f[r] (g^(1,0))[r,r2]].
In real problem, I have the function of four variables and mixed partial derivatives, so it would be great if there is some generic way to prescribe all of function's derivatives as Real.
calculus-and-analysis functions function-construction symbolic complex
edited Sep 22 at 19:14
kglr
163k8188387
asked Sep 22 at 18:02
Thela Hun Ginjeet
445
add a comment |Â
up vote
2
down vote
favorite
Re and Im work properly, with appropriate assumptions, in the example like this
Assuming[g[_, _] ∈ Reals, Simplify[Im[3*I*g[r, r2] + 45]]]
On the other hand, if the derivative of the function is also present, similar approach does not work
Assuming[(r | g[_, _] | D[g[_, _], _]) ∈ Reals, Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
i.e. does not give back 3*D[g[r, r2], r]
More dramatically,
Assuming[(r | g[_, _] | f[_]) ∈ Reals, Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
gives 3 Re[g[r,r2] (f^′)[r]+f[r] (g^(1,0))[r,r2]].
In real problem, I have the function of four variables and mixed partial derivatives, so it would be great if there is some generic way to prescribe all of function's derivatives as Real.
calculus-and-analysis functions function-construction symbolic complex
edited Sep 22 at 19:14
kglr
163k8188387
asked Sep 22 at 18:02
Thela Hun Ginjeet
445
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Re and Im work properly, with appropriate assumptions, in the example like this
Assuming[g[_, _] ∈ Reals, Simplify[Im[3*I*g[r, r2] + 45]]]
On the other hand, if the derivative of the function is also present, similar approach does not work
Assuming[(r | g[_, _] | D[g[_, _], _]) ∈ Reals, Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
i.e. does not give back 3*D[g[r, r2], r]
More dramatically,
Assuming[(r | g[_, _] | f[_]) ∈ Reals, Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
gives 3 Re[g[r,r2] (f^′)[r]+f[r] (g^(1,0))[r,r2]].
In real problem, I have the function of four variables and mixed partial derivatives, so it would be great if there is some generic way to prescribe all of function's derivatives as Real.
calculus-and-analysis functions function-construction symbolic complex
edited Sep 22 at 19:14
kglr
163k8188387
asked Sep 22 at 18:02
Thela Hun Ginjeet
445
Re and Im work properly, with appropriate assumptions, in the example like this
Assuming[g[_, _] ∈ Reals, Simplify[Im[3*I*g[r, r2] + 45]]]
On the other hand, if the derivative of the function is also present, similar approach does not work
Assuming[(r | g[_, _] | D[g[_, _], _]) ∈ Reals, Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
i.e. does not give back 3*D[g[r, r2], r]
More dramatically,
Assuming[(r | g[_, _] | f[_]) ∈ Reals, Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
gives 3 Re[g[r,r2] (f^′)[r]+f[r] (g^(1,0))[r,r2]].
In real problem, I have the function of four variables and mixed partial derivatives, so it would be great if there is some generic way to prescribe all of function's derivatives as Real.
calculus-and-analysis functions function-construction symbolic complex
calculus-and-analysis functions function-construction symbolic complex
edited Sep 22 at 19:14
kglr
163k8188387
asked Sep 22 at 18:02
Thela Hun Ginjeet
445
edited Sep 22 at 19:14
kglr
163k8188387
asked Sep 22 at 18:02
Thela Hun Ginjeet
445
edited Sep 22 at 19:14
kglr
163k8188387
edited Sep 22 at 19:14
kglr
163k8188387
edited Sep 22 at 19:14
kglr
163k8188387
163k8188387
asked Sep 22 at 18:02
Thela Hun Ginjeet
445
asked Sep 22 at 18:02
Thela Hun Ginjeet
445
asked Sep 22 at 18:02
Thela Hun Ginjeet
445
445
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
Use the FullForm of the derivatives:
Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals,
Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals,
Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
answered Sep 22 at 18:48
kglr
163k8188387
1
Great, it works! FormDerivative[_, _][g][_, _]allows for generalizing to arbitrary number of derivatives.
– Thela Hun Ginjeet
Sep 23 at 10:50
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Use the FullForm of the derivatives:
Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals,
Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals,
Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
answered Sep 22 at 18:48
kglr
163k8188387
1
Great, it works! FormDerivative[_, _][g][_, _]allows for generalizing to arbitrary number of derivatives.
– Thela Hun Ginjeet
Sep 23 at 10:50
add a comment |Â
up vote
3
down vote
accepted
Use the FullForm of the derivatives:
Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals,
Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals,
Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
answered Sep 22 at 18:48
kglr
163k8188387
1
Great, it works! FormDerivative[_, _][g][_, _]allows for generalizing to arbitrary number of derivatives.
– Thela Hun Ginjeet
Sep 23 at 10:50
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Use the FullForm of the derivatives:
Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals,
Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals,
Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
answered Sep 22 at 18:48
kglr
163k8188387
Use the FullForm of the derivatives:
Assuming[(r | g[_, _] | Derivative[1, 0][g][_, _]) ∈ Reals,
Simplify[Im[3*I*D[g[r, r2], r] + 45]]]
Assuming[(r | g[_, _] | f[_] | Derivative[1, 0][g][_, _] | Derivative[1][f][_]) ∈ Reals,
Simplify[Im[3*I*(D[g[r, r2]*f[r], r]) + 45]]]
answered Sep 22 at 18:48
kglr
163k8188387
edited Sep 22 at 20:17
answered Sep 22 at 18:48
kglr
163k8188387
answered Sep 22 at 18:48
kglr
163k8188387
answered Sep 22 at 18:48
kglr
163k8188387
163k8188387
1
Great, it works! FormDerivative[_, _][g][_, _]allows for generalizing to arbitrary number of derivatives.
– Thela Hun Ginjeet
Sep 23 at 10:50
add a comment |Â
1
Great, it works! FormDerivative[_, _][g][_, _]allows for generalizing to arbitrary number of derivatives.
– Thela Hun Ginjeet
Sep 23 at 10:50
1
1
Great, it works! Form
Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.– Thela Hun Ginjeet
Sep 23 at 10:50
Great, it works! Form
Derivative[_, _][g][_, _] allows for generalizing to arbitrary number of derivatives.– Thela Hun Ginjeet
Sep 23 at 10:50
add a comment |Â
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