Expression of type Norm

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 Variable
from proveit.linear_algebra import Norm, ScalarMult, VecAdd
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = Norm(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _phase)), ket1))))

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 \|\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\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: 15 operands: 4
4	ExprTuple	5, 6
5	Operation	operator: 21 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	28, 10
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 35 operands: 13
11	Operation	operator: 24 operand: 18
12	Operation	operator: 15 operands: 16
13	ExprTuple	37, 17
14	ExprTuple	18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Operation	operator: 35 operands: 23
20	Operation	operator: 24 operand: 28
21	Literal
22	ExprTuple	28, 37
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28
26	Literal
27	Operation	operator: 29 operands: 30
28	Literal
29	Literal
30	ExprTuple	37, 31, 32, 33, 34
31	Literal
32	Literal
33	Operation	operator: 35 operands: 36
34	Literal
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Variable