from the theory of proveit.physics.quantum.QPE¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import l
from proveit.logic import Equals
from proveit.numbers import Add, Mod, ModAbs, subtract
from proveit.physics.quantum.QPE import _b_floor, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = Equals(ModAbs(subtract(Mod(Add(_b_floor, l), _two_pow_t), _b_floor), _two_pow_t), ModAbs(l, _two_pow_t)).with_wrapping_at(2)

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\begin{array}{c} \begin{array}{l} \left|\left(\left(b_{\textit{f}} + l\right) ~\textup{mod}~ 2^{t}\right) - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} =  \\ \left|l\right|_{\textup{mod}\thinspace 2^{t}} \end{array} \end{array}

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()(2)('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 17
6Literal
7ExprTuple23, 17
8Operationoperator: 18
operands: 9
9ExprTuple10, 11
10Operationoperator: 12
operands: 13
11Operationoperator: 14
operand: 22
12Literal
13ExprTuple16, 17
14Literal
15ExprTuple22
16Operationoperator: 18
operands: 19
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple22, 23
20Literal
21ExprTuple24, 25
22Literal
23Variable
24Literal
25Literal