VerifySolutions

VerifySolutions

is an option to Solve and related functions that controls whether to verify solutions.

Details

  • VerifySolutions controls whether the solutions obtained using non-equivalent transformations or numerical methods should be verified.
  • Possible settings include:
  • Automaticautomatically determine whether to verify
    Trueattempt to verify
    Falsedo not verify

Examples

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Basic Examples  (1)

Solve an equation:

Use VerifySolutions to check if they are solutions or not:

Scope  (4)

Solve verifies solutions obtained using non-equivalent transformations:

With VerifySolutions False, Solve does not verify the solutions:

Some of the solutions returned with VerifySolutions False are not correct:

Use a fast numeric test in an attempt to select correct solutions:

In this case, numeric verification gives the correct solution set:

Reduce returns only the correct solutions:

Solve an equation symbolically without verifying the solution:

This can yield solutions that are not mathematically valid:

Solve the same equation numerically:

Note the unverified solutions do not satisfy the given equation:

Verifying the solution discards the invalid result, returning an empty list indicating there are no solutions:

Using Automatic solution verification attempts to detect and discard possibly invalid results:

Properties & Relations  (1)

Using Solve without solution verification can give mathematically incorrect results:

Using Reduce will return False if no solutions exist:

Wolfram Research (1988), VerifySolutions, Wolfram Language function, https://reference.wolfram.com/language/ref/VerifySolutions.html.

Text

Wolfram Research (1988), VerifySolutions, Wolfram Language function, https://reference.wolfram.com/language/ref/VerifySolutions.html.

CMS

Wolfram Language. 1988. "VerifySolutions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VerifySolutions.html.

APA

Wolfram Language. (1988). VerifySolutions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VerifySolutions.html

BibTeX

@misc{reference.wolfram_2024_verifysolutions, author="Wolfram Research", title="{VerifySolutions}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/VerifySolutions.html}", note=[Accessed: 21-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_verifysolutions, organization={Wolfram Research}, title={VerifySolutions}, year={1988}, url={https://reference.wolfram.com/language/ref/VerifySolutions.html}, note=[Accessed: 21-January-2025 ]}