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

# build up the expression from sub-expressions
expr = Exp(Exp(e, Add(Neg(frac(Mult(two, pi, i, m), _two_pow_t)), 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}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot m}{2^{t}} + \left(2 \cdot \pi \cdot \mathsf{i} \cdot \varphi\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: 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 operands: 8
7	Literal
8	ExprTuple	9, 10
9	Operation	operator: 11 operand: 14
10	Operation	operator: 20 operands: 13
11	Literal
12	ExprTuple	14
13	ExprTuple	27, 24, 25, 15
14	Operation	operator: 16 operands: 17
15	Literal
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	27, 24, 25, 26
22	Literal
23	ExprTuple	27, 28
24	Literal
25	Literal
26	Variable
27	Literal
28	Literal