Functions, Operators & Constants¶
The Following Functions, Operators and Constants are defined and useable in Expression Strings.
Note
All names are case-senitive
Constants¶
Constants are basicaly unchanging global variabes, an used to define special values
| Name | Version Added | Value |
|---|---|---|
| pi | 1.0 | Pi (\(\pi\)) |
| e | 1.0 | Euler’s number (\(\mathrm{e}\)) |
| Inf | 1.0 | Infinity (\(\infty\)) |
| NaN | 1.0 | Not a Number |
| h | 1.1 | Plancks Constant (\(h\)) [1] |
| hbar | 1.1 | Reduced Plancks Constant (\(\hbar\)) [1] |
| m_e | 1.1 | Electron Mass (\(m_{\rm e}\)) [1] |
| m_p | 1.1 | Proton Mass (\(m_{\rm p}\)) [1] |
| m_n | 1.1 | Neturon Mass (\(m_{\rm n}\)) [1] |
| c | 1.1 | Speed of Light (\(c\)) [1] |
| N_A | 1.1 | Avogardo’s Number (\(N_{\rm A}\)) [1] |
| mu_0 | 1.1 | Magnetic Constant (\(\mu_0\)) [1] |
| eps_0 | 1.1 | Electric Constant (\(\varepsilon_0\)) [1] |
| k | 1.1 | Boltzmann Constant (\(k_\mathrm{b}\)) [1] |
| G | 1.1 | Gravitational Constant (\(G\)) [1] |
| g | 1.1 | Standard Accleration due to gravity (\(\mathrm{g}\)) [1] |
| q | 1.1 | Elementary Charge (\(\mathit{e}\)) [1] |
| R | 1.1 | Ideal Gas Constant (\(R\)) [1] |
| sigma | 1.1 | Stefan-Boltzmann Constant (\(\sigma\)) [1] |
| Rb | 1.1 | Rydberg Constant (\(R_\infty\)) [1] |
| [1] | (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16) Requires scipy to use these constants |
Operators¶
Operators are special function maped to a symbol, that will appear between the operands rather than as a name folloed by a comma seperated list of operands.
Operators have a Precedence this indicate the Priotiy with which they are applied i.e. low Precedence valued operators will be evaluated before higher valued ones.
Note
Values of the same Precedence are evaluated left to right
| Symbol | Operation | Syntax | Precedence | Display |
|---|---|---|---|---|
| + | Added A to B | A + B | 3 | \(\left(A + B\right)\) |
| - | Subtract B from A | A - B | 3 | \(\left(A - B\right)\) |
| * | Mutlipy A by B | A * B | 2 | \(\left(A \times B\right)\) |
| / | Divide A by B | A / B | 2 | \(\frac{A}{B}\) |
| % | Reminder of A Divided by B | A % B | 2 | \(\left(A \bmod B\right)\) |
| ^ | Raise A to the B’th power | A ^ B | 1 | \(A^{B}\) |
| & | Logical AND of A and B | A & B | 4 | \(\left(A \land B\right)\) |
| | | Logical OR of A and B | A | B | 4 | \(\left(A \lor B\right)\) |
| <\> | Logical XOR of A and B | A <\> B | 4 | \(\left(A \oplus B\right)\) |
| ! | Logical NOT of A | !A | UNARY | \(\neg A\) |
| == | Test if A is equal to B | A == B | 5 | \(\left(A = B\right)\) |
| ~ | Test if A is similar to B | A ~ B | 5 | \(\left(A \sim B\right)\) [2] |
| != | Test if A isn’t equal to B | A != B | 5 | \(\left(A \neq B\right)\) |
| !~ | Test if A isn’t similar to B | A !~ B | 5 | \(\left(A \nsim B\right)\) [2] |
| < | Test if A is less than to B | A < B | 5 | \(\left(A < B\right)\) |
| > | Test if A is more than to B | A > B | 5 | \(\left(A > B\right)\) |
| <= | Test if A is less than or equal to B | A < B | 5 | \(\left(A \leq B\right)\) |
| >= | Test if A is more than or equal to B | A > B | 5 | \(\left(A \geq B\right)\) |
| <~ | Test if A is less than or similar to B | A < B | 5 | \(\left(A \lesssim B\right)\) [2] |
| >~ | Test if A is more than or similar to B | A > B | 5 | \(\left(A \gtrsim B\right)\) [2] |
| [2] | (1, 2, 3, 4) Check it values are very close rather then just equal, i.e. 1 is similar to 1.000001 but not equal (see Equation.similar Module) |
Functions¶
These as normal functions a name followed by a list of parameters
| Name | Operation | Syntax | Display |
|---|---|---|---|
| abs | Absolute value of A | abs(A) | \(\left|A\right|\) |
| sin | Sine value of A | sin(A) | \(\sin\left(A\right)\) |
| cos | Cosine value of A | cos(A) | \(\cos\left(A\right)\) |
| tan | Tangent value of A | tan(A) | \(\tan\left(A\right)\) |
| re | Real Compoent of A | re(A) | \(\Re\left(A\right)\) |
| im | Imagery Compoent of A | im(A) | \(\Im\left(A\right)\) |
| sqrt | Square root of A | sqrt(A) | \(\sqrt{A}\) |
Examples¶
The Following are some example expressions demonstrating the Precedence order and display formating
sin(x*(y+z))
sin((x * (y + z)))
\[\sin\left(\left(x \times \left(y + z\right)\right)\right)\]
(a+b)/(c+d)
((a + b) / (c + d))
\[\frac{\left(a + b\right)}{\left(c + d\right)}\]
a+b/c+d*e^f
((a + (b / c)) + (d * (e ^ f)))
\[\left(\left(a + \frac{b}{c}\right) + \left(d \times e^{f}\right)\right)\]
a^b/c^d
((a ^ b) / (c ^ d))
\[\frac{a^{b}}{c^{d}}\]
a*b/c*d
(((a * b) / c) * d)
\[\left(\frac{\left(a \times b\right)}{c} \times d\right)\]
a*b/(c*d)
((a * b) / (c * d))
\[\frac{\left(a \times b\right)}{\left(c \times d\right)}\]
