Expression of type Equals

from the theory of proveit.numbers.multiplication

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, delta, k, theta
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, e, i, pi, two

# build up the expression from sub-expressions
sub_expr1 = Add(a, b)
sub_expr2 = Mult(two, pi, i, b)
expr = Equals(Mult(sub_expr1, Exp(e, Mult(two, pi, i, k, delta)), Exp(e, Mult(two, pi, i, theta, k)), Exp(e, sub_expr2)), Mult(sub_expr1, Exp(e, Add(Mult(Add(Mult(two, pi, i, delta), Mult(two, pi, i, theta)), k), sub_expr2)))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left(a + b\right) \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \delta} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\right) =  \\ \left(\left(a + b\right) \cdot \mathsf{e}^{\left(\left(\left(2 \cdot \pi \cdot \mathsf{i} \cdot \delta\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot \theta\right)\right) \cdot k\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot b\right)}\right) \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 38 operands: 5
4	Operation	operator: 38 operands: 6
5	ExprTuple	10, 7, 8, 9
6	ExprTuple	10, 11
7	Operation	operator: 16 operands: 12
8	Operation	operator: 16 operands: 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 33 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	21, 18
13	ExprTuple	21, 19
14	ExprTuple	21, 27
15	ExprTuple	20, 32
16	Literal
17	ExprTuple	21, 22
18	Operation	operator: 38 operands: 23
19	Operation	operator: 38 operands: 24
20	Variable
21	Literal
22	Operation	operator: 33 operands: 25
23	ExprTuple	41, 42, 43, 31, 40
24	ExprTuple	41, 42, 43, 44, 31
25	ExprTuple	26, 27
26	Operation	operator: 38 operands: 28
27	Operation	operator: 38 operands: 29
28	ExprTuple	30, 31
29	ExprTuple	41, 42, 43, 32
30	Operation	operator: 33 operands: 34
31	Variable
32	Variable
33	Literal
34	ExprTuple	35, 36
35	Operation	operator: 38 operands: 37
36	Operation	operator: 38 operands: 39
37	ExprTuple	41, 42, 43, 40
38	Literal
39	ExprTuple	41, 42, 43, 44
40	Variable
41	Literal
42	Literal
43	Literal
44	Variable