MaplePrimes - Questions, Posts, help, musings, answers ... all things Maple and math

Ask a Question

Create a Post

MaplePrimes Announcement

Introducing VerifyTools

by: aroche 285 Product: Maple

August 21 2024

5 1

VerifyTools is a package that has been available in Maple for roughly 24 years, but until now it has never been documented, as it was originally intended for internal use only. Documentation for it will be included in the next release of Maple. Here is a preview:

VerifyTools is similar to the TypeTools package. A type is essentially a predicate that a single expression can either satisfy or not. Analogously, a verification is a predicate that applies to a pair of expressions, comparing them. Just as types can be combined to produce compound types, verifications can also be combined to produce compund verifications. New types can be created, retrieved, queried, or deleted using the commands AddType, GetType (or GetTypes), Exists, and RemoveType, respectively. Similarly in the VerifyTools package we can create, retrieve, query or delete verifications using AddVerification, GetVerification (or GetVerifications), Exists, and RemoveVerification.

The package command VerifyTools:-Verify is also available as the top-level Maple command verify which should already be familiar to expert Maple users. Similarly, the command VerifyTools:-IsVerification is also available as a type, that is,

VerifyTools:-IsVerification(ver);

will return the same as

type(ver, 'verification');

The following examples show what can be done with these commands. Note that in each example where the Verify command is used, it is equivalent to the top-level Maple command verify. (Also note that VerifyTools commands shown below will be slightly different compared to the Maple2024 version):

>	with(VerifyTools):

Suppose we want to create a verification which will checks that the length of a result has not increased compared to the expected result. We can do this using the AddVerification command:

>	AddVerification(length_not_increased, (a, b) -> evalb(length(a) <= length(b)));

First, we can check the existence of our new verification and get its value:

>	Exists(length_not_increased);

>	GetVerification(length_not_increased);

For named verifications, IsVerification is equivalent to Exists (since names are only recognized as verifications if an entry exists for them in the verification database):

>	IsVerification(length_not_increased);

On the other hand, a nontrivial structured verification can be checked with IsVerification,

>	IsVerification(boolean = length_not_increased);

whereas Exists only accepts names:

>	Exists(boolean = length_not_increased);

Error, invalid input: VerifyTools:-Exists expects its 1st argument, x, to be of type symbol, but received boolean = length_not_increased

The preceding command using Exists is also equivalent to the following type call:

>	type(boolean = length_not_increased, verification);

Now, let's use the new verification:

>	Verify(x + 1/x, (x^2 + 1)/x, length_not_increased);

>	Verify((x^2 + 1)/x, x + 1/x, length_not_increased);

Finally, let's remove the verification:

>	RemoveVerification(length_not_increased);

>	Exists(length_not_increased);

>	GetVerification(length_not_increased);

Error, (in VerifyTools:-GetVerification) length_not_increased is not a recognized verification

GetVerifications returns the list of all verifications known to the system:

>	GetVerifications();

Download VerificationTools_blogpost.mw

Austin Roche
Software Architect
Mathematical Software
Maplesoft

Read Full Post

Featured Post

sija

Rolling a plane curve...

Hello!

I present a simple work-up of rolling a plane curve along a fixed plane curve in 2d space. Maple sources are attached.

Kind regards!

Source.zip

September 10

5 10

Read Full Post

Featured Post

one man

1270

Circle inscribed between...

Circles inscribed between curves can be specified by a system of equations relative to the coordinates of the center of the circle and the coordinates of the tangent points. Such a system can have 5 or 6 equations and 6 variables, which are mentioned above.
In the case of 5 equations, we can immediately obtain an infinite set of solutions by selecting the ones we need from it.
(See the attached text for more details.)
The 1st equation is responsible for the belonging of the point of tangency to one of the curves.
The 2nd equation is responsible for the belonging of the point of tangency to another curve.
In the 3rd equation, the points of tangency on the curves belong to the inscribed circle.
In the 4th and 5th equations, the condition is satisfied that the tangents to the curves are perpendicular to the radii of the circle at the points of contact.
The 6th equation serves either to find a specific inscribed circle or to find an infinite set of solutions. It is selected based on the type of curves and their mutual arrangement.

In this example, we search for a subset of the solution set using the Draghilev method by solving the first five equations of the system: we inscribe circles in two "angles" formed by the intersection of the exponent and the ellipse.
The text of this example, its solution in the form of a picture,"big" option and pictures of similar examples.
INSCRIBED_CIRCLES.mw

Addition 09/01/24,
One curve for the first two equations in coordinates x1,x2 and x3,x4
f1:= x1^2 - 2.5*x1*x2 + 3*x2^2 - 1;
f2:= x3^2 - 2.5*x3*x4 + 3*x4^2 - 1;