2 Using Maxima. features important for qinf $.$

The package is loaded using the load^$\dagger$function like this

There are several tutorials and manuals available for Maxima. Here is a very brief one focused on aiding the introduction to the qinf package. We will not give examples of matrices until later, but point out that the notation for matrix multiplication in Maxima is a dot , eg. A . B. If $A$ is a $m\times n$ matix and $B$ a $p\times q$ matrix, then A . B is a $n\times p$ matrix. The inner product of quantum state vectors, the outer product (dyad) of quantum state vectors, the composition of operators, and the mapping of one vector to another by an operator are all special cases of matrix multiplication and are all represented by the dot (along with conjugation in the case of the inner and outer products.) The remaining product, the tensor product, becomes the Kronecker product in the matrix representation of a finite dimensional Hilbert space. To agree with standard terminology, we introduce the infix operator otimes and the function tensor_product that eventually call the Maxima function kronecker_product . See the section on matrices in the Maxima manual.

Maxima can use exact real and complex numbers or the standard floating point approximations, or arbitrary precision floating point numbers. Numerical expressions are simplified upon entry. Each input line must be terminated by a semicolon (some interfaces do this automatically) or by a dollar sign, which suppresses the output.

Assignment is denoted by a colon while function definitions are denoted by := For example, a : b+c ; evaluates b+c and assigns the result to a. On the other hand a(x,y) := x^y ; defines the function $a(x,y)$.

We suppress the output here with a dollar sign because it's big- $51$ terms.

Some exact numbers and floating point approximations.

Defining and using a function.

Complex numbers. %i is the identifier for $i=\sqrt{-1}$.

Some special numbers are defined, such as %pi and %e.