Expression of type Mult

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

# build up the expression from sub-expressions
expr = Mult(Exp(a, k), Exp(Mult(Exp(e, Mult(two, pi, i, theta)), Add(a, b)), k), Exp(e, Mult(two, pi, 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())

a^{k} \cdot \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta} \cdot \left(a + b\right)\right)^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}

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.	()	()	('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',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 23 operands: 1
1	ExprTuple	2, 3, 4
2	Operation	operator: 15 operands: 5
3	Operation	operator: 15 operands: 6
4	Operation	operator: 15 operands: 7
5	ExprTuple	21, 9
6	ExprTuple	8, 9
7	ExprTuple	19, 10
8	Operation	operator: 23 operands: 11
9	Variable
10	Operation	operator: 23 operands: 12
11	ExprTuple	13, 14
12	ExprTuple	25, 26, 27, 22
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	Operation	operator: 23 operands: 24
21	Variable
22	Variable
23	Literal
24	ExprTuple	25, 26, 27, 28
25	Literal
26	Literal
27	Literal
28	Variable