CLI Syntax

> [:ALG] :OP {:OPERANT1} {:OPERANT2}

Remark

> appears automatically at the start of each round of dialogue. Don't type it manually.

Brackets ([] and {}) are necessary in order to ensure parser works properly. Because we allow whitespaces present inside a formula of :OPERANT, the parser cannot tell where to truncate between arguments without brackets' help.

:ALG and :OP are not case-sensitive. As to :OPERANTS, keep x in polynomial and i in complex numbers in lowercase, otherwise the parser may throw an error.

Examples

Here we omit the outputs. I advise you have a look at the examples section, where host much more instances with output attached.

> [Z] Add {1} {2}
> [Q] Div {4/7} {6/13}
> [F(13)] Sub {0} {2}
> [QPol] Divmod {9x^2+12x+1} {x+3}
> [FPol(7)] Bezout {6x^4 + x^3 + 2} {x^5 + 5x^13 + 4}
> [Zi] Mul {18 + 3i} {7i + 16}

:ALG

Currently, six algebraic structures are supported, divided into two categories, rings and fields. See the parse page for a detailed description on how commands take effect mathematically in each case.

Fields:

Q, F(p)

Here, Q stands for rationals. F(p) is the finite field of p elements, in which p must be specified as a positive prime number. F(13), F(19) are accepted, while F(10), F(0), F(-7), and F() are not.

Rings:

Z, Zi, QPol, FPol(p)

Z stands for integers. QPol means polynomials with rational coefficients. FPol(p) means polynomial with F(p) coefficients.

Zi means Gaussian integers, namely all complex numbers a+bi such that a and b are integers.

:OP

:OP means operations. In some sense, it's the main component of a command. Following are all supported arguments:

Add, Sub, Mul, Div, Divmod, Bezout

Add, Sub, Mul mean addition (+), subtraction (-), multiplication (*) respectively. They are available for any :ALG.

Div, division (/), only makes sense if :ALG is a field. If the second operand is zero, it returns a error.

Similarly, Divmod and Bezout are valid only if :ALG is a ring. Divmod evaluates the Euclidean division, outputing a quotient and a remainder. If the second operand is zero, it errs. Bezout returns the triple in Bézout's identity.

:OPERANT

:OPERANT means numbers that engage in an operation. So far, all operations take exactly two operants. Future features may drop this requirement.

Depending on your choice of :ALG, the parser uses different strategies to read it. The rules of formatting operants are specified in the parse section.