Visitar URL original
GeneratedParameters—Wolfram Documentation

WOLFRAM

Wolfram Language & System Documentation Center

GeneratedParameters

is an option that specifies how parameters generated to represent the results of various symbolic operations should be named.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
See Also
Tech Notes
History
Cite this Page

GeneratedParameters

GeneratedParameters

is an option that specifies how parameters generated to represent the results of various symbolic operations should be named.

Details

  • The typical default setting is GeneratedParameters->C.
  • The setting GeneratedParameters->f specifies that successive generated parameters should be named f[1], f[2], ….
  • In typical cases, the f[i] are used to parameterize families of solutions to equations.
  • The f[i] usually correspond to free parameters, but are also sometimes used to represent arbitrary functions.
  • The f[i] have indices that start at 1 for each invocation of a particular symbolic operation.
  • GeneratedParameters->(Module[{C},C]&) guarantees that parameters are unique, even across different invocations of a function.
  • GeneratedParameters is an option to such functions as DSolve, RSolve, and Reduce.

Examples

open all close all

Basic Examples  (4)

General solution of algebraic equation:

Wolfram Language code: Reduce[Sin[x] == 1, x]

General solution of differential equation:

Wolfram Language code: DSolve[y''[x] == 4y[x], y[x], x]

General solution of difference equation:

Wolfram Language code: RSolve[a[n + 2] == 4a[n], a[n], n]

General expression for an indefinite integral:

Wolfram Language code: Integrate[1 / (x ^ 2 + 1), x, GeneratedParameters -> C]

Scope  (5)

Special solutions:

Wolfram Language code: Reduce[Sin[x] == 1, x] /. C[1] -> 1
Wolfram Language code: DSolve[y''[x] == 4y[x], y[x], x] /. {C[1] -> 1, C[2] -> 2}
Wolfram Language code: RSolve[a[n + 2] == 4a[n], a[n], n] /. {C[1] -> 1, C[2] -> 2}

Use a different symbol:

Wolfram Language code: Reduce[Sin[x] == 1, x, GeneratedParameters -> α]

Use a subscripted symbol:

Wolfram Language code: DSolve[y''[x] == 4y[x], y[x], x, GeneratedParameters -> (Subscript[c, #]&)]

Start index at 0:

Wolfram Language code: RSolve[a[n + 2] == 4a[n], a[n], n, GeneratedParameters -> (C[# - 1]&)]

General solution to partial differential equation:

Wolfram Language code: DSolve[y D[u[x, y], x] + x D[u[x, y], y] == -4 x y u[x, y], u, {x, y}]

Special solution:

Wolfram Language code: u[x, y] /. First[%] /. C[1] -> Function[z, Exp[-2z]]
Wolfram Language code: Plot3D[%, {x, -2, 2}, {y, -2, 2}]
Wolfram Research (2003), GeneratedParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/GeneratedParameters.html.

Text

Wolfram Research (2003), GeneratedParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/GeneratedParameters.html.

CMS

Wolfram Language. 2003. "GeneratedParameters." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeneratedParameters.html.

APA

Wolfram Language. (2003). GeneratedParameters. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeneratedParameters.html

BibTeX

@misc{reference.wolfram_2026_generatedparameters, author="Wolfram Research", title="{GeneratedParameters}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/GeneratedParameters.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_generatedparameters, organization={Wolfram Research}, title={GeneratedParameters}, year={2003}, url={https://reference.wolfram.com/language/ref/GeneratedParameters.html}, note=[Accessed: 14-November-2026]}