Expression of type Abs

from the theory of proveit.trigonometry

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, b, r
from proveit.numbers import Abs, Exp, Mult, e, i, subtract

# build up the expression from sub-expressions
expr = Abs(subtract(Mult(r, Exp(e, Mult(i, a))), Mult(r, Exp(e, Mult(i, b)))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left|\left(r \cdot \mathsf{e}^{\mathsf{i} \cdot a}\right) - \left(r \cdot \mathsf{e}^{\mathsf{i} \cdot b}\right)\right|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 24 operands: 8
7	Operation	operator: 9 operand: 12
8	ExprTuple	16, 11
9	Literal
10	ExprTuple	12
11	Operation	operator: 19 operands: 13
12	Operation	operator: 24 operands: 14
13	ExprTuple	22, 15
14	ExprTuple	16, 17
15	Operation	operator: 24 operands: 18
16	Variable
17	Operation	operator: 19 operands: 20
18	ExprTuple	26, 21
19	Literal
20	ExprTuple	22, 23
21	Variable
22	Literal
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Variable