Expression of type Mult

from the theory of proveit.physics.quantum.QPE

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 k
from proveit.numbers import Exp, Mult, Neg, e, i, pi, two
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = Mult(Exp(e, Neg(Mult(two, pi, i, k, _phase))), Exp(e, Mult(two, pi, i, _phase, k)))

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())

\mathsf{e}^{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \varphi\right)} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}

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: 14 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	8, 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operand: 13
8	Literal
9	Operation	operator: 14 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	16, 17, 18, 20, 19
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17, 18, 19, 20
16	Literal
17	Literal
18	Literal
19	Variable
20	Literal