Expression of type Exp

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, m
from proveit.numbers import 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 = Exp(Exp(e, Neg(frac(Mult(two, pi, i, Mod(m, _two_pow_t)), _two_pow_t))), 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}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot \left(m ~\textup{mod}~ 2^{t}\right)}{2^{t}}})^{k}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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