::mfp::math::calculus::deri_ridders(4) :

deri_ridders(expr, var, val, ord) calculate ord-order derivative value of expression expr which is based on variable var when the variable's value is equal to val. This function always uses Ridders method. For example, deri_ridders("x**2+x","x",3,2) returns 2.

::mfp::math::calculus::derivative(2) :

derivative(expression, variable) calculate derivative of expression which is based on variable. Note that both expression and variable must be strings. For example, derivative("x**2+x","x") returns a string based expression which is "2*x+1".

::mfp::math::calculus::derivative(4) :

derivative(expr, var, val, method) calculate derivative value of expression expr which is based on variable var when the variable's value is equal to val. The parameter method selects the method to use. True means using Ridders method while false means simply calculating derivative expression value at val. For example, derivative("x**2+x","x",2,true) returns 5.

::mfp::statement::evaluate(1...) :

evaluate(expr_string,var_string1,var_value1,var_string2,var_value2, ...) returns the value of string based expression expr_string when the string based variable var_string1 equals var_value1, variable var_string2 equals var_value2, ... respectively. Note that var_value1, var_value2, ... can be any type and the number of variables can be zero, i.e. evaluate("3+2") is valid.

::mfp::statement::expr_to_string(1) :

expr_to_string(expr) converts a string based expression expr to a string. Any defined function in the expression will be converted to its full name (i.e. citingspace followed by function name). For example, expr_to_string("pwd()") will be converted to "::mfp::io::file::pwd()" while expr_to_string("pwd(1, 2)") will be converted to "pwd(1,2)" because pwd function with zero parameter is defined while there is no pwd function with two parameters.

::mfp::math::calculus::integrate(2) :

integrate(x,y) returns the indefinite integrated expression of expression x based on variable y where x and y are both strings. Note that if x cannot be indefinitely integrated or x is too complicated to solve, this function will throw an exception.

::mfp::math::calculus::integrate(4) :

integrate(x,y,z,w) returns the integrated value of expression x based on variable y changing from z to w. Note that x and y are string type and z and w can be real numbers, complex numbers or strings. The integrating algorithm selected is adaptive Gauss-Kronrod method.

::mfp::math::calculus::integrate(5) :

integrate(x,y,z,w,v) returns integrated value given a string expression x of a variable y (also a string type) and an interval [z, w]. In calculation, one step length is (w - z)/v, note that v must be a positive integer while w and z can be real numbers, complex values or strings. If v is zero, this function is the same as integrate(x,y,z,w).

::mfp::math::calculus::lim(3) :

lim(expr, var, dest_value) calculates the limit value of expression expr when variable var is closing to dest_value. expr and var should be string and dest_value can be expression or value, whether string based or not. For example, lim("1/x", "x", 0) or lim("(x+2)/(x+3)","x","3+0"). Note that this function is still under development.

::mfp::math::stat_stoch::product_over(3) :

product_over(x, y, z) calculates the product of string based expression x over integer value y to z. Note that y and z are also string based value, y should be written like "a=10" (where a is the variable) and z should be like "20". For example, product_over("x+1", "x=1", "10").

::mfp::math::stat_stoch::sum_over(3) :

sum_over(x, y, z) calculates the sum of string based expression x over integer value y to z. Note that y and z are also string based value, y should be written like "a=10" (where a is the variable) and z should be like "20". For example, sum_over("x+1", "x=1", "10").