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 l
from proveit.numbers import Add, Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t, _two_pow_t__minus_one

# build up the expression from sub-expressions
expr = Exp(Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t)))), Add(_two_pow_t__minus_one, one))

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}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)})^{\left(2^{t} - 1\right) + 1}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 32 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 32 operands: 4
3	Operation	operator: 16 operands: 5
4	ExprTuple	6, 7
5	ExprTuple	8, 21
6	Literal
7	Operation	operator: 9 operands: 10
8	Operation	operator: 16 operands: 11
9	Literal
10	ExprTuple	34, 12, 13, 14
11	ExprTuple	31, 15
12	Literal
13	Literal
14	Operation	operator: 16 operands: 17
15	Operation	operator: 24 operand: 21
16	Literal
17	ExprTuple	19, 20
18	ExprTuple	21
19	Operation	operator: 22 operand: 26
20	Operation	operator: 24 operand: 27
21	Literal
22	Literal
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Literal