Expression of type InSet

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 m
from proveit.logic import InSet
from proveit.numbers import Complex, Exp, Mod, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _two_pow_t

# build up the expression from sub-expressions
expr = InSet(Exp(e, Neg(frac(Mult(two, pi, i, Mod(m, _two_pow_t)), _two_pow_t))), Complex)

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}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot \left(m ~\textup{mod}~ 2^{t}\right)}{2^{t}}} \in \mathbb{C}

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',)
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: 23 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Literal
7	Operation	operator: 8 operand: 10
8	Literal
9	ExprTuple	10
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 22
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	25, 16, 17, 18
16	Literal
17	Literal
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Literal
26	Literal