Description
Creates an answer evaluator which checks expressions defining functions.
Syntax
fun_cmp(function_string, options)
fun_cmp([fun_str1, fun_str2], options)
Params
The first argument is the expression defining the correct function, or
one or more expressions placed in square brackets. The options are
specified in key => value pairs. (see Options)
Options
| Option key | Option value | Default | | var | either the number of variables or a reference to an array of variable names | ['x', 'y'] | | limits | reference to an array of arrays of limits | [[0,1],[0,1]] | | mode | 'std' (default) (function must match exactly)
'antider' (function must match up to a constant) | 'std' | | relTol | a number indicating the relative tolerance (as a percentage) for checking each point | .01 per cent | | tol | an absolute tolerance for checking error | | | numPoints | the number of points to evaluate the function at | 4 | | params | an array of "free" parameters which can be
used to adapt the correct answer to the submitted answer. (e.g. ['c']
for a constant of integration in the answer x^3/3 + c ). | [''] | | maxConstantOfIntegration | maximum size of the constant of integration and other free parameters. (prevents numerical overload) | 10**100 | | debug | 1 to obtain additional warning messages for debugging, 0 to turn off | 0 |
Returns
One (or more) answer evaluators for expressions defining functions
Examples
* fun_cmp('x^2 +3x') checks that the submitted expression matches this quadratic.
* fun_cmp('t^2- sin(t)', var => 't')
* fun_cmp('t^2 - sin(t)', vars => ['t'], limits => [-4,4]). You can also use limits => [[-4,4]] for consistency
* fun_cmp('x^2 + y^2', vars => ['x', 'y'],
limits => [[-4,4],[-2,6]], numPoints => 10 )
* fun_cmp('x^2 + y^2 + c', vars => ['x', 'y'], params =>['c'],
limits => [[-4,4],[-2,6]], numPoints => 10 ) will match 'x^2 +y^2 + 25'.
* fun_cmp( 'cos(x) + a*e^(-x) + b*e^(2x)', params =>['a', 'b']) will accept a linear family of solutions, e.g. solution set to a linear ODE
* fun_cmp( 'x^2 +sin(c*x)' , params =>['c'])
will NOT work. The expressions have to be linear in the parameters (but
of course they can be non-linear in the variables such as x).
Notes
The options can be used in any combination that makes sense, and probably some that don't. One exception: reltol and tol cannot be used together.
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