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, Mult, e, frac, i, pi, subtract, two
from proveit.physics.quantum.QPE import _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Exp(Exp(e, Mult(Mult(two, pi, i), subtract(_phase, frac(m, _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}^{\left(2 \cdot \pi \cdot \mathsf{i}\right) \cdot \left(\varphi - \frac{m}{2^{t}}\right)})^{k}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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