Expression of type Abs

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 Abs, Exp, Mult, e, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t

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

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())

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

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix

# display the expression information
stored_expr.expr_info()

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