hypergeon0
http://www.math.kobe-u.ac.jp/OCD/hypergeon0.tfb
2003-11-11
experimental
2002-11-11, 2003-11-30
1
1
arith1
linalg1
linalg4
linalg5
quant1
relation1
set1
This CD defines some supplementary symbols necessary for hypergeon1
and hypergeon2 (hypergeometric series of n variables).
These symbols may be included in CD's linalg, logic, poly, and set.
plus_part
The argument is a vector. It replaces negative elements in the vector
to zero.
minus_part
The argument is a vector. It replaces positive elements in the vector
to zero and negative elements to their absolute values.
$u = u_{+} - u_{-}$
kernel
It returns the kernel of the map defined by a matrix in a specified
domain.
$\kernel(D,A) = \{ x \in D | A x = 0 \}$
1
where
The word "where" is often used in mathematical expressions
to set variables or to say side conditions.
CDname logic1.implies can be used for these purposes, but
"where" will be more intuitive and more friendly expression
for authors.
$x^n=x x x \where{n=3}$
3
multi_power
multi_power is for using the multi-index notation.
$x^e = \prod_{i=1}^n x_i ^ {e_i}$
1
cartesian_product_n
the cartesian product of n copies of the first argument.
Binary function.
$ Z^m \times Z^n = Z^{m+n} $