#h
Plank constant
Js
#e
Electron Charge
C
#na
Avagadro Number
mol
-1
#R
Gas constant
J/K/mol
#hp
Mechanical horsepower
W
Matrices
Reckon interprets vectors that look like matrices as matrices. The vector
[1 2 3]
is considered as a row, for
example, it legal to multiply this row by a 3xN matrix. For matrix multiplication of
A*B
, the number of
columns of
A
must match the number of rows of
B
.
The column vector of 1,2,3 looks like this:
[[1][2][3]]
and is very different. You can generate this column by
transposing the vector
T([1 2 3])
. For RPN transpose is mapped to
SHIFT ARROW
Note
that currently you must separate elements of vectors or matrices by commas during the input
process.
Currently, if Reckon does not see your input as a valid matrix it will treat it as a generic vector. This might
cause confusion. For example the 1x1 matrix of
0
is the vector
[0]
, consequently
[[0]]
is not recognised as
this object and will not operate arithmetically.
Once an object is recognised as a matrix, Reckon tries to treat it arithmetically as far as possible, If you add
or multiply a vector or matrix by a scalar, the effect will be to apply that operation on each element of the
vector. e.g.
[[1 2][3 4]] + 1
is
[[2 3][4 5]]
.
If you add vectors, corresponding elements will be added. eg
[1 2 3] + [4 5 6]
is
[5 7 9].
The same applies
to matrices, eg
[[1 2][3 4]] + [[4 5][6 7]]
is
[[5 7][9 11]]
.
Multiplication of matrices works according to the usual rules:
[[1 2][3 4]] * [[4 5][6 7]]
is
[[16 19]
[36 43]]
Reckon tries to offer division of matrices by defining A/B as B
-1
*A. i.e., Reckon calculates the inverse of the
matrix B and multiplies it in order to give the illusion of division
1
1
Matrices form a ring and not a field, proper division does not really exist!
.
for example
[[1 2][3 4]]/[[4 5][6 7]]
is
[[4 3]
[-3 -2]]
Other matrix operations including the determinant which is given by
Abs()
, and transpose which is
T()
.
The
Proot()
function finds the roots of a polynomial with real coefficients. For example,
5𝑧𝑧
6
− 45𝑧𝑧
5
+ 225𝑧𝑧
4
− 425𝑧𝑧
3
+ 170𝑧𝑧
2
+ 370𝑧𝑧 − 500
Proot
takes a vector of coefficients where element
i
is the coefficient of z
i
.
Note
the order of coefficients in
the input vector.
eg.
> proot([-500,370,170,-425,225,-45,5])
[3-4i 3+4i 1-1i 1+1i 2 -1]
